3/6/16, 9:32 AM
533574755
College Physics 1
Website:

Assignments
http://people.rit.edu/abesps1
PLEASE SIGN THE ATTENDANCE SHEET
GO TO MY WEBSITE…
https://people.rit.edu/abesps1
www.masteringphysics.com
PAGE 1 OF 50
3/6/16, 9:32 AM
College Physics 1 (211)
Email abesps1@rit.edu
Schedule
Day
Mon
Tues
Wed
Thursday
Friday**
533574755
PAGE 2 OF 50
Instructor: Dr. Alan Entenberg, Office 8-3206, 475-5148 (office), 475-2421 (Physics Dept.),
Website for course www.rit.edu/~abesps1
Website for HW www.masteringphysics.com
Tentative
Lecture
Office hours* Sect 04 and 05
2:00 – 2:50 PM 4:00 – 6:00 Noon, 8-3305
2:00 – 2:50 PM
2:00 – 2:50 PM
2:00 – 2:50 PM
2:00 – 2:50 PM (Bates Study Center, COS)
Workshop
Section 04
Workshop
Section 05
4:00 – 6:00 PM, 8-3345 6:00 – 8:00 PM, 8-3345
4:00 – 6:00 PM, 8-3345 6:00 – 8:00 PM, 8-3345
*Office hours: You are welcome to come by at anytime. One on one meetings in my office can be scheduled if you are unable to make the above
posted office hours.
**Office hour will be in the College of Science Bates Study Center. The Center is open every day and is staffed by physics faculty, graduate students, and
upper level physics majors. The schedule of the Center is posted on the door.
MORE HELP from Academic Support Center: www.rit.edu/asc See this link for tutoring in Math and Physics in room 01-2371.
Monday (10-7), Tuesday (10-9), Wednesday (10-9), Thursday (10-4), Friday (10-2)
Course Prerequisites: Competency in algebra, geometry, and trigonometry and passing grade in College Physics 1
Course Goals
(1) Understand and use derived concepts of force, energy, and momentum based on the fundamental concepts of matter, space, and time.
(2) Describe motion of an object in horizontal and/or “free-fall” motions near the surface of the earth.
Course Text: COLLEGE PHYSICS: A Strategic Approach by Knight, Jones, and Field, Pearson/Addison Wesley, 2007.
Chapter 1
Concepts of Motion and Mathematical Background
Read: Sections 1 – 7
Chapter 2
Motion in One Dimension
Read: Sections 1 – 7
Chapter 3
Vectors and Motion in Two Dimensions
Read: Sections 1 – 8
Chapter 4
Forces and Newton’s Laws of Motion
Read: Sections 1 – 8
Chapter 5
Applying Newton’s Laws
Read: Sections 1 – 5, 6 – 8 wait!
Chapter 6
Circular Motion, Orbits, and Gravity
Read: Sections 1 – 7
Chapter 7
Rotational Motion
Read: Sections 1 – 6
Chapter 8
Equilibrium and Elasticity
Read: Sections 1 – 4
Chapter 9
Momentum
Read: Sections 1 – 7
Chapter 10
Energy and Work
Read: Sections 1 – 10
Homework: You will be assigned about ten problems each week. Some of these will be from the HW website www.masteringphysics.com associated with your
text.
3/6/16, 9:32 AM
533574755
PAGE 3 OF 50
Grading (VERY TENTATIVE WEIGHTING):
A ( > 90%)
B ( > 80%)
C ( > 65%)
D ( > 55%)
Homework
15 %
Exams 1, 2, 3 (lowest replaced by Final Exam)
50 %
Exam1 - March 31, 2008
Final Exam
20 %
Cumulative
Activities –
15 %
Attendance
???
Bonus points (for catching my mistakes made in class)
Each point worth about 0.1% on course average).
A FORMULA SHEET WILL BE SUPPLIED FOR EACH EXAM and FOR the joint common FINAL EXAM.
Makeup policy-- It is not possible to makeup an exam. The lowest exam is replaced by the final exam.





MAKEUP MUST BE SCHEDULED IN ADVANCE
IMMEDIATE NOTIFICATION OF A VERIFIABLE ILLNESS
Your academic advisor must also contact me and explain!
It is not possible to makeup an activity. The lowest activity will be dropped.
WHEN POSSIBLE, AN OPPORTUNITY TO DO THE ACTIVITY WILL BE GIVEN.
There is a automatic online deduction of 10% for each day that a homework assignment is late.
3/6/16, 9:32 AM
Lecture/
Workshop
Date
L1
3/10/08
W1
3/11/08
W2
3/13/08
L2
3/17/08
W3
3/18/08
W4
3/20/08
L3
3/24/08
W5
3/25/08
W6
3/27/08
L4
3/31/08
W7
4/1/08
W8
4/3/08
L5
W9
4/7/08
4/8/08
W10
4/10/08
L6
4/14/08
W11
4/15/08
533574755
PAGE 4 OF 50
Schedule and Equipment Needs
Introduction to the course. Discuss units; conversion of units; dimensional analysis; displacement; average velocity; average acceleration; and
motion diagrams (1D only).
“Estimation”
“Unit conversion”
“Basic Measurements and Uncertainties Homework” due
Discuss uncertainties and error analysis.
“Basic Measurements and Uncertainties”
Need: 14 aluminum cylinders of varying volumes, 7 triple beam balances, 7 rulers, 7 electronic calipers
Discuss instantaneous velocity; instantaneous acceleration; position versus time, velocity versus time, and acceleration versus time graphs;
trigonometry; vectors and scalars; and 2D kinematics.
“Position-Time and Velocity-Time graphs”
“Logger Pro Tutorial” due
“Introduction to LabPro and the Force Sensor”
Need 14: force sensors with hook, 50 g hangers, mass sets
“Acceleration and Deceleration (1D)”
“Motion diagrams and Motion Graphs”
Discuss free-body diagrams; the gravitational force; the normal force; the tension force; the frictional force; and the spring force. Use “One
Dimensional Forces, Translational Equilibrium, Free Body Diagrams” activity as part of discussion.
“Ball Drop Homework” due
DEMO: “Penny/feather”, need apparatus with pump
DEMO: two balls – one dropped and the other fired horizontally, need apparatus
“Ball Drop”
Need 14: motion detectors and small, well inflated soccer balls
“Vector Algebra and Static Translational Equilibrium Homework” due
“Vector Algebra and Static Translational Equilibrium”
Need: 14 force tables (already set up), 14 mass sets, lots of small 1 g, 2 g, etc. masses for use in determining uncertainty in hanging mass
Exam 1. Discuss Newton’s laws.
“Interaction Forces”
Need: 2 force sensors attached to low friction carts, one 500 g mass bar, and one 1.2 m short track per group
“Newton’s Second Law”
Need 14 set ups: accelerometer attached to force sensor which is attached to a low friction cart (arrow on accelerometer points away from force
sensor hook), short track
Discuss uniform circular motion; universal gravitation; and non-uniform circular motion.
“Newton’s Second Law Problems”
“Motion in 2D (circular track)”
Need 42: rulers and protractors
Exam 2. Discuss rotational kinematics.
“Uniform Circular Motion”
Need 14: centripetal force apparatus (already set up), stop watches, rulers, 50 g hangers, mass sets,
3/6/16, 9:32 AM
W12
4/17/08
L7
4/21/08
W13
4/22/08
W14
4/24/08
L8
4/28/08
W15
4/29/08
W16
5/1/08
L9
5/5/08
W17
5/6/08
W18
5/8/08
L10
5/12/08
5/13/08
W19
W20
5/15/08
533574755
PAGE 5 OF 50
Need: 7 digital scales, lots of small 1 g, 2 g, etc. masses for use in determining uncertainty in hanging mass
“Rotational Kinematics”
Need 14: RMS with aluminum disk attached, crash box
Need: 7 blue mass sets, spools of string, scissors
Discuss torque; center-of-gravity; moment of inertia; Newton’s second law in rotational form; torque and equilibrium; the spring force; and stress
and strain. Use “Torque Calculation” activity as part of discussion.
“Torque and Moment of Inertia”
Need 14: RMS with aluminum disk attached, crash box, calipers, rulers
Need: 7 blue mass sets, 7 digital scales, and spools of string
“Torque and Equilibrium”
Need 14: meter sticks with drilled holes, 0-5 N and 0-50 N spring scales, 50 g hangers
Need: spools of string, scissors, masking tape
Discuss impulse; linear momentum; conservation of linear momentum; inelastic collisions; angular momentum; and conservation of angular
momentum.
“Angular Momentum - Qualitative”
Need: 7 low friction bike wheels, 7 platforms, two 500 g mass bars
Discuss work; kinetic energy; work-kinetic energy theorem; work done by gravity; work done by an applied force; and conservative forces. Use
“Conservative and Non-conservative Forces” activity as part of discussion.
Exam 3. Discuss potential energy; mechanical energy; mechanical energy conservation; work done by variable forces; and elastic potential
energy.
“Energy Graphs”
DEMO: “Rotational energy and Rolling Motion”
Need set up of two inclined planes; hoop/disk of same radius rolling down one incline and back up another.
“Energy Conservation”
Need 14: RMS with aluminum disk attached, crash box
Need: 7 blue mass sets, spools of string, scissors
Discuss energy in collisions and power.
“Rotational Collision”
Need 14: RMS with two aluminum disks and specialty brass pin, rulers
Need: 7 digital scales
Open (“One Dimensional Collision”?)
3/6/16, 9:32 AM
533574755
PAGE 6 OF 50
Notation
FF
Components FX
+
Magnitude and Angle
and
FY +
F=|F| >0
and +
3/6/16, 9:32 AM
533574755
PAGE 7 OF 50
3/6/16, 9:32 AM

533574755
PAGE 8 OF 50
What is a single “force” on a given object by a given source?
 A force is a “push” or a “pull” on an object of mass M.
Object of mass M
Push
F
Pull
F
F
Force is a “vector quantity.”
Force has “magnitude”
Force has “direction”
Note: The “tail” of the force vector will usually show where the force acts on the
object.
3/6/16, 9:32 AM
533574755
PAGE 9 OF 50
Two types of forces
 1. Contact forces
Normal force
Tension force
One object touches another object
FN
N
Ft
T
Friction force
o Static friction
fs
o Kinetic friction or sliding friction
fk
3/6/16, 9:32 AM
533574755
Two types of forces
PAGE 10 OF 50
continued
 2. Action at a distance forces
force seems to act through “empty space”
o Gravitational force
Fg
Wt  " weight of object"
o Electric and magnetic forces “interaction forces between charges”
Fundamental particles electron, proton, neutron
More fundamental
proton and neutron are composites of quarks
o Nuclear (strong) and nuclear (weak) forces
3/6/16, 9:32 AM
533574755
PAGE 11 OF 50
PRINCIPLE OF LINEAR SUPERPOSITION FOR FORCES
What is a “net force” on an object?

    
Fnet   F  F1  F2  F3  F4  
 All of the forces on an object add instantaneously to a single net force.
 The “resultant force” or “net force” is obtained in the same way a resultant
displacement vector is obtained.
NOTE: ZERO NET FORCE DOES NOT MEAN THERE ARE NO FORCES ON AN OBJECT!!
 Parallelogram rule for only 2 forces
 Pretend force vectors are same as displacement vectors when adding
3/6/16, 9:32 AM
533574755
PAGE 12 OF 50
NEWTON’S FIRST LAW:
 ENABLES US TO DETERMINE WHETHER THERE IS A “NET
FORCE” ON AN OBJECT.
(paraphrased below by abe)
EXPERIMENTAL FACT “An object in motion (constant velocity) stays in motion
(constant velocity) unless acted upon by a net force.”
 The constant velocity is non-zero.
EXPERIMENTAL FACT “An object at rest stays at rest unless acted upon by a
net force.”
 The constant velocity can even be zero.
“If there is a net force on an object, the velocity must change, i.e., the object must accelerate.”
3/6/16, 9:32 AM
533574755
PAGE 13 OF 50
NEWTON’S THIRD LAW: ALL FORCES OCCUR IN PAIRS!!
 “THERE IS NO SUCH THING AS AN ISOLATED FORCE!!”
3/6/16, 9:32 AM
533574755
PAGE 14 OF 50
Ball #1 moves to the right toward Ball #2
Ball #2 is initially at rest
#1
#2
Force on #2 by #1
Force on #1 by #2
Note:
Magnitudes are equal
F21 = F12
#1
#2
At the instant of contact, each ball exerts a force on the other. The pair of forces is called an “action and
reaction” pair of forces. Ignore gravitational effects for this example.
QUESTION: CAN YOU TOUCH SOMEONE WITHOUT BEING TOUCHED YOURSELF?
Your Name (Print):
Group Members:
Date:
Group:
3/6/16, 9:32 AM
533574755
PAGE 15 OF 50
Interaction Forces (Modified)
You will explore the relationship between the forces that two interacting objects exert on each
other.
A force is a push or pull that one body exerts on another. When two bodies interact, they exert
forces on each other. When you push down on the table with your hand, the table pushes up on your
hand, an effect you can feel. This pushing force is an example of a contact force since the two
objects are in contact with each other. As another example, when you drop a pencil, the earth exerts
a gravitational force on the pencil pulling it vertically down while the pencil exerts an upward force
on the earth. This gravitational force is an example of a non-contact force (or a so called “action-ata-distance” force) since the two objects do not have to be in physical contact in order to exert the
force. Isolated forces do not exist; forces always exist in pairs. Nothing can exert a force without
having a force exerted on it.
PREDICTION
Two objects, a truck on the left and a car on the right, can move on a horizontal surface. When
the truck and car are in contact, there is a horizontal contact force between them, meaning that the
truck pushes on the car and the car pushes on the truck. All motion is along a straight line. You are
to compare the magnitudes of these two forces in the different situations described in Table 1.
In parts (a) through (d), assume the vehicles are of equal weight. In parts (e) through (i), assume
the truck is much heavier than the car. Discuss and debate your predictions with the others in your
group until you reach a consensus. Record the group’s consensus decision in the second column of
Table 1 using “less than” (<), “greater than” (>) or “equal to” (=) signs.
3/6/16, 9:32 AM
533574755
Name _____________________________
PAGE 16 OF 50
Contact Force on truck by car
Contact Force on car by truck
Attach at least one graphical
measurement from your team’s
observations
Table 1:
Summary of Predictions and Measurements regarding
magnitudes of forces (insert the correct algebraic sign: >, = or <)
(a) Equal weights; truck (active) pushes against car (passive) but there is
no motion.
(b) Equal weight; car (active) pushes against truck (passive) but there is
no motion.
(c) Equal weight; Truck (more active) pushes car (passive) to the right,
both are moving to the right.
(d) Equal weight; Car (more active) pushes truck (passive) to the left,
both are moving to the left.
(e) Heavy truck (active) pushes on light car (passive) to the right but there
is no motion.
(f) Light car (active) pushes on heavy truck (passive) to the left but there
is no motion.
(g) Heavy truck (more active) moves to the right and collides with a light car
(passive) that is at rest (in neutral). They separate after the collision.
PREDICTION MEASUREMENT
Magnitude of the
(performed after
all Predictions
Force on truck by
car is
are recorded)
( > , = or < )
the magnitude of
the
Force on car by
truck
Explain Reasoning below
3/6/16, 9:32 AM
533574755
PAGE 17 OF 50
MEASUREMENT:
 Connect two force sensors to CH1 and CH2 of the LabPro interface.
 Connect the LabPro interface to the computer.
 Define the truck as the sensor connected to CH1, and the car as the sensor connected to CH2.
 Be sure the slide switch on the force sensors is at +50 N.
 Open the Logger Pro software. Manually set up the sensors if they do not auto-ID.
 Reverse the sign of sensor #1 (Experiment->Set Up Sensors->Show All Interfaces, left click the CH1
sensor icon, check Reverse Direction).
 Calibrate the sensors using weights corresponding to approximately 1000 g and 500 g suspended from
the hook attached to each sensor. Remember to include the mass of the hanger and to convert the mass in
grams to a force in Newtons. Replace the hook on each force sensor with a rubber bumper provided by your
instructor.
 Zero both sensors (Ctrl-0) and check the zero by collecting data with the sensors horizontal and not
touching.
Push on each bumper with your hand while collecting data to see how data is collected and displayed.
 Each force sensor should be securely attached to a low-friction cart that is free to roll along the 1.2 m
track.
Be sure that neither cart rolls off the end of the track. Now set up experiments to check the results you
predicted in parts (a) to (i).
Record all your observations regarding the magnitudes of the forces in the third column in the Table 1.
 (a) - (b)
Place the force sensors on the table and push them together in such a way that there is no
movement.
Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in
Table 1.
Using Print Graph, Print one graph per group for either part (a) or part (b);
append the last names of all members of your group to the bottom of the graph.
Be sure the graph includes a title (right click the graph ->Graph Options) and a description.
3/6/16, 9:32 AM
533574755
 (c) Push on the truck to the right while it is in contact with the car.
PAGE 18 OF 50
Hold the car firmly - imagine the car’s brakes are applied, yet the truck still moves the car to the right.
Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in
Table 1.
(d) Push the car to the left while it is in contact with the truck.
Hold the truck firmly - imagine the truck’s brakes are applied, yet the car still moves the truck to the left.
Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in
Table 1.
 Add at least one 500 g mass bar to the cart attached to sensor #1 (the truck). Check parts (e) and (f)
of your predictions.
(e) - (f) Repeat measurements similar to parts (a) and (b). Record the results in Table 1.
For one of the experiments (e) or (f), print one graph per group (append the last names of all members of
your group to the bottom of the graph). Be sure the graph includes a title and a description.
 To check your predictions during collisions when the truck and/or the car are initially moving,
you must decrease the time of data collection to 5 s and increase the data sampling rate to 1000
samples/second.
Click Experiment -> Data Collection. Change the length of data collection to 5 s and the sampling rate to
1000 samples per second.
Click Done. Check parts (g) - (i) of your predictions.
The graphical display will take a few moments before displaying due to the large amount of data
collected.
(g) - (i) Gently push the carts as required. Collect data and Autoscale.
Change the minimum and maximum values on the time axis so the display includes the
time interval from just before the collision to a time just after the collision.
To change the maximum value on the time axis,
3/6/16, 9:32 AM
533574755
PAGE 19 OF 50
place the cursor near enough to the largest number on the horizontal scale until the cursor changes shape to an
“I”, click,
then type the appropriate number and hit Enter. Repeat for the smallest number on the horizontal axis.
Compare the magnitude of the forces and record your observations in Table 1.
Remember to return the time axis to the 0 s to 5 s range after each experiment.
For one of the experiments (g) through (i),
print one graph per group (append the last names of all members of your group to the bottom of the graph).
Be sure the graph includes a title and a description.
Reconcile your predictions with your measurements: In what ways were your predictions different from your
measurements? In what ways were they the same?
This activity is designed to help you learn something about the forces that two objects exert on each other. The
result is known as Newton’s Third Law of Motion. Use the space below to write a clear summary about what
you have discovered regarding the interaction force between two objects.
3/6/16, 9:32 AM
Your Name (Print):
Group Members:
533574755
PAGE 20 OF 50
Date:
Group:
Interaction Forces
You will explore the relationship between the forces that two interacting objects exert on each other.
A force is a push or pull that one body exerts on another. When two bodies interact, they exert forces on each other. When you push down on the table with your hand, the
table pushes up on your hand, an effect you can feel. This pushing force is an example of a contact force since the two objects are in contact with each other. As another example,
when you drop a pencil, the earth exerts a gravitational force on the pencil pulling it vertically down while the pencil exerts an upward force on the earth. This gravitational force is
an example of a non-contact force (or a so called “action-at-a-distance” force) since the two objects do not have to be in physical contact in order to exert the force. Isolated forces
do not exist; forces always exist in pairs. Nothing can exert a force without having a force exerted on it.
PREDICTION
Two objects, a truck on the left and a car on the right, can move on a horizontal surface. When the truck and car are in contact, there is a horizontal contact force between
them, meaning that the truck pushes on the car and the car pushes on the truck. All motion is along a straight line. You are to compare the magnitudes of these two forces in the
different situations described in Table 1.
In parts (a) through (d), assume the vehicles are of equal weight. In parts (e) through (i), assume the truck is much heavier than the car. Discuss and debate your predictions
with the others in your group until you reach a consensus. Record the group’s consensus decision in the second column of Table 1 using “less than” (<), “greater than” (>) or
“equal to” (=) signs.
3/6/16, 9:32 AM
533574755
PAGE 21 OF 50
Table 1: Summary of Predictions and Measurements regarding magnitudes of forces (insert the correct algebraic sign: >, = or <)
PREDICTION
Magnitude of the force of
car on truck is (>, = or
<)
the magnitude of the
force of truck on car
MEASUREMENT
(performed after
all Predictions
are recorded)
(a) Equal weight; truck pushes against car but there is no motion.
(b) Equal weight; car pushes against truck but there is no motion.
(c) Equal weight; truck pushes car to the right, both are moving to
the right.
(d) Equal weight; car pushes truck to the left, both are moving to
the left.
(e) Heavy truck pushes on light car to the right but there is no
motion.
(f) Light car pushes on heavy truck to the left but there is no
motion.
(g) Heavy truck moves to the right and collides with a light car that
is at rest (in neutral). They separate after the collision.
(h) Light car moves to the left and collides with a heavy truck that is
at rest (in neutral). They separate after the collision.
(i) Heavy truck moves to the right and collides with a light car that is
moving to the left. They separate after the collision.
Summarize your “PREDICTIONS” by describing the reason(s) you chose the predicted responses.
3/6/16, 9:32 AM
533574755
PAGE 22 OF 50
MEASUREMENT:
Connect two force sensors to CH1 and CH2 of the LabPro interface. Connect the LabPro interface to the computer. Define the truck as the sensor connected to CH1, and the car
as the sensor connected to CH2. Be sure the slide switch on the force sensors is at +50 N.
Open the Logger Pro software. Manually set up the sensors if they do not auto-ID. Reverse the sign of sensor #1 (Experiment->Set Up Sensors->Show All Interfaces, left click
the CH1 sensor icon, check Reverse Direction). Calibrate the sensors using weights corresponding to approximately 1000 g and 500 g suspended from the hook attached to each
sensor. Remember to include the mass of the hanger and to convert the mass in grams to a force in Newtons. Replace the hook on each force sensor with a rubber bumper provided
by your instructor. Zero both sensors (Ctrl-0) and check the zero by collecting data with the sensors horizontal and not touching. Push on each bumper with your hand while
collecting data to see how data is collected and displayed.
Each force sensor should be securely attached to a low-friction cart that is free to roll along the 1.2 m track. Be sure that neither cart rolls off the end of the track. Now set up
experiments to check the results you predicted in parts (a) to (i). Record all your observations regarding the magnitudes of the forces in the third column in the Table 1.
(a) - (b)
(c)
(d)
Place the force sensors on the table and push them together in such a way that there is no movement. Collect data and Autoscale if necessary. Compare the magnitude
of the forces and record your observations in Table 1. Using Print Graph, Print one graph per group for either part (a) or part (b); append the last names of all
members of your group to the bottom of the graph. Be sure the graph includes a title (right click the graph ->Graph Options) and a description.
Push on the truck to the right while it is in contact with the car. Hold the car firmly - imagine the car’s brakes are applied, yet the truck still moves the car to the right.
Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in Table 1.
Push the car to the left while it is in contact with the truck. Hold the truck firmly - imagine the truck’s brakes are applied, yet the car still moves the truck to the left.
Collect data and Autoscale if necessary. Compare the magnitude of the forces and record your observations in Table 1.
Add at least one 500 g mass bar to the cart attached to sensor #1 (the truck). Check parts (e) and (f) of your predictions.
(e) - (f)
Repeat measurements similar to parts (a) and (b). Record the results in Table 1. For one of the experiments (e) or (f), print one graph per group (append the last
names of all members of your group to the bottom of the graph). Be sure the graph includes a title and a description.
To check your predictions during collisions when the truck and/or the car are initially moving, you must decrease the time of data
collection to 5 s and increase the data sampling rate to 1000 samples/second. Click Experiment -> Data Collection. Change the length of data
collection to 5 s and the sampling rate to 1000 samples per second. Click Done. Check parts (g) - (i) of your predictions. The graphical
display will take a few moments before displaying due to the large amount of data collected.
(g) - (i)
Gently push the carts as required. Collect data and Autoscale. Change the minimum and maximum values on the time axis so the display includes the time interval
from just before the collision to a time just after the collision. To change the maximum value on the time axis, place the cursor near enough to the largest number
on the horizontal scale until the cursor changes shape to an “I”, click, then type the appropriate number and hit Enter. Repeat for the smallest number on the
horizontal axis. Compare the magnitude of the forces and record your observations in Table 1. Remember to return the time axis to the 0 s to 5 s range after each
experiment. For one of the experiments (g) through (i), print one graph per group (append the last names of all members of your group to the bottom of the graph).
Be sure the graph includes a title and a description.
Reconcile your predictions with your measurements: In what ways were your predictions different from your measurements? In what ways were they the same?
This activity is designed to help you learn something about the forces that two objects exert on each other. The result is
known as Newton’s Third Law of Motion. Use the space below to write a clear summary about what you have discovered
regarding the interaction force between two objects.
3/6/16, 9:32 AM
533574755
PAGE 23 OF 50
NEWTON’S SECOND LAW: PROVIDES US WITH AN OPERATIONAL DEFINITION OF A NET
FORCE.

Fnet  M a
Vector equation
Fnet = M a
Magnitude equation

    
Fnet   F  F1  F2  F3  F4  
Two observations
Observation #1: For a fixed acceleration, force is proportional to “acceleration” or “rate of
velocity change”
Force  acceleration
Note:  or “alpha” means “proportional to”
o How would you design an experiment to test this statement?
Use a stretched spring to define a “unit of force” F0
For a fixed mass M, measure acceleration for 1 spring, 2 springs, 3 springs, etc. Plot
acceleration a versus F = N F0 to see if F and a are linearly proportional.
Observation #2: For a fixed acceleration, force is proportional to “mass”
Force  Mass
o How would you design an experiment to test this statement?
Start with the gravitational field at the earth’s surface; this will provide a constant
acceleration
Determine the force on an object of mass M, 2 M, 3 M, etc. Plot mass (M, 2 M, 3 M, …)
versus force (F, 2 F, 3 F, …) to see if there is a linear relationship.
3/6/16, 9:32 AM
533574755
PAGE 24 OF 50
NEWTON’S SECOND LAW: PROVIDES US WITH AN OPERATIONAL DEFINITION OF A NET
FORCE.
SUMMARY

Fnet  M a
Vector equation
Fnet = M a
Magnitude equation

    
Fnet   F  F1  F2  F3  F4  
 The force on an object is proportional to the acceleration of the object. (The
greater the velocity change per unit time, the bigger the force.)
 To obtain the same acceleration with a bigger mass, a bigger force is
required.
UNITS….
 SI Unit
 CGS Unit
 BE Unit
the Newton
the dyne
the pound
N = kg m/s2
g cm/s2
slug ft/s2
3/6/16, 9:32 AM
533574755
PAGE 25 OF 50
The Force of Gravity
Consider an object in “free gall” at the Earth’s surface.

The acceleration has magnitude |a| = g = +9.80 m/s2 in the downward direction. Hence,
there is a gravitational force on the object
“Magnitude and angle vector description”
Magnitude: Fg = M a = M g = “Wt” the weight of the object
Direction:
“Down”
“Component vector description”
X component:
FX = M aX = 0
Y component:
FY = M aY = – M g
Y axis
aX = 0
aY = – g where g = + 9.80 m/s2
a
Note that with respect to the y axis which points
upward, aY = - g = - 9.80 m/s2 and aX = 0
F
3/6/16, 9:32 AM
533574755
PAGE 26 OF 50
FREE BODY DIAGRAMS AND FREE BODY EQUATIONS FOR STATIC EQUILIBRIUM
IN ONE DIMENSION…
Newton’s 2nd Law for linear motion
 Fx = M ax
or
FnetX = M ax
Translational static equilibrium
where FnetX =  Fx

ACCELERATION IS ZERO!!!! HENCE…
 Fx = M ax = 0
 Examples
DO EACH IN CLASS!

An object at rest on a flat table
Show that FN = M g

An object hanging from a rope
Show that Ft = M g

An object at rest on an incline
Show that FN = M g cos

Other examples
3/6/16, 9:32 AM
Your Name (Print):
Group Members:
533574755
PAGE 27 OF 50
Date:
Group:
Newton’s Second Law


Fnet  m a
You will explore the relationship between the net force applied to an object and the object’s resulting acceleration.
Cart
A
B
Velocity
PREDICTION
You pull a low-friction cart along a straight horizontal track, as shown in Figure 1. The
cart starts from rest at point A and stops at point B, a distance of approximately 75 cm. You
never let go of the cart. The cart only moves to the right.
Time
On the grids to the right, carefully sketch the Velocity of
the cart as a function of Time and the Position of the cart as a
function of Time. THE TIME AXES ARE IDENTICAL.
Remember that velocity is a vector – be careful with its
algebraic sign.
Position
Figure 1 Cart pulled along straight horizontal line from point A to point B
Time
533574755
PAGE 28 OF 50
The cart starts from rest at point A, moves only to the right,
and stops at point B. On the grid to the right, sketch a graph of
the resulting Acceleration of the cart versus Time.
Acceleration
3/6/16, 9:32 AM
Time
THE TIME AXES ARE IDENTICAL. Remember that force and
acceleration are vectors – be careful with algebraic signs.
Force
BASED ON YOUR ACCELERATION-TIME SKETCH,
carefully sketch the horizontal Force applied to the cart as a
function of Time.
Time
3/6/16, 9:32 AM
533574755
PAGE 29 OF 50
In the grid below, sketch a predicted graph of Force versus Acceleration. Force and
acceleration are vectors – be careful with algebraic signs.
Why do you expect this particular shape? What would happen to the shape of the curve if the
mass of the cart were increased?
Force
Acceleration
3/6/16, 9:32 AM
533574755
PAGE 30 OF 50
MEASUREMENT
This activity is your first introduction to an electronic accelerometer: The “Low-g
Accelerometer” measures acceleration along the line marked by the arrow on the label (a “singleaxis” accelerometer). The accelerometer can measure accelerations in the range of -5g to +5g,
where one g is the magnitude of the earth’s gravitational acceleration (g = 9.80 m/s2). The
accelerometer also senses the effect of gravity and uses this property to calibrate the sensor.
The accelerometer is attached to a force sensor which is attached to a low friction cart. Be certain
the arrow on the accelerometer is parallel to the long side of the force sensor and points away from
the force sensor hook. The force sensor must be set to the ±10 N range. Connect the force sensor to
channel 1 (CH1) and the accelerometer to channel 2 (CH2) on the interface.
An experiment file is available for this activity. From the desktop, click on Start then on
My Computer. Double click on the Student Shares on ‘svphy01’ (S:) folder. Open the College
Physics Students folder and then open Team Physics 211. Select and drag the experiment file titled
Newton’s Second Law into the My Documents folder. Close the My Computer folder and launch the
experiment file from the My Documents folder. Click OK if you receive a sensor error message
(“Sensors specified in experiment file do not match detected sensors”). When properly configured,
two graphs (Force versus Time and Acceleration versus Time) should be displayed.
Ignore: “The sensors should not need to be calibrated.” If your instructor recommends you
calibrate the sensors, then follow the calibration procedure outlined below.
Calibrate the force sensor – Suspend the sensor assembly vertically and use approximately 500 g
and 1000 g masses as the force calibration points. Remember to include the mass of the hanger and
to convert the mass in grams to a force in Newtons.
3/6/16, 9:32 AM
533574755
PAGE 31 OF 50
Calibrate the accelerometer - Suspend the accelerometer at rest with the arrow pointing
vertically up. Define this calibration point as +9.80 m/s2. Suspend the accelerometer at rest with
the arrow pointing vertically down and define this calibration point as -9.80 m/s2.
Place the sensor assembly horizontal and at rest. Press the TARE button on the side of the
force sensor. When the sensor readings stabilize, zero the sensors (Ctrl 0). Repeat this process
prior to collecting any experimental data.
Starting with the cart initially at rest, Collect data, pull on the force sensor hook and move the cart
back and forth along a straight line. Do not let go of the force sensor. Pull in such a way that your
forearm is HORIZONTAL and PARALLEL to the track. Pick up and move the sensor cables
with the cart. Don’t let any cables or other material obstruct the motion of the cart. Good
results are obtained with accelerations in the range -5 m/s2 to +5 m/s2. A schematic of the setup is
shown in Figure 2.
Accelerometer
Force
Sensor
Cart
Figure 2 Cart with sensors attached
Print a copy of the observed Force versus Time and Acceleration versus Time graphs. Append the
names of all participating group members to the graph. Be sure the graph is carefully labeled.
3/6/16, 9:32 AM
533574755
PAGE 32 OF 50
Describe the observed relationship between the Force-Time and the Acceleration-Time graphs.
Change one of the graphs to display Force versus Acceleration (Force on the vertical axis and
Acceleration on the horizontal axis). Based on this graph, what can you conclude about the
relationship between the applied force and the resulting acceleration? Remember, force and
acceleration are vectors.
Explain how your measured Force-Acceleration graph compares to your predicted ForceAcceleration graph. How are they similar; how are they different?
Determine and record the slope of the linear portion of the Force-Acceleration line (INCLUDE
UNCERTAINTY AND UNITS). Note that you will need to sort the acceleration data before you
can perform the fit.
Write (and simplify) the slope’s units in terms of the basic SI units (the “Newton” is a derived unit).
What physical quantity does the slope correspond to?
3/6/16, 9:32 AM
533574755
PAGE 33 OF 50
Print a copy of the observed Force-Acceleration graph with the curve fitting parameter box clearly
displayed (and not covering any relevant portion of the graph). Click on the Force-Acceleration
graph and use Print Graph. Append the names of all participating group members to the graph. Be
sure the graph is carefully labeled.
DESIGN AND PERFORM a measurement to verify your hypothesis regarding the physical
significance of the slope. Clearly describe the experimental procedure and include NUMERICAL
results supporting your hypothesis.
Summarize the results of this activity in the context of Newton’s Second Law.
3/6/16, 9:32 AM
533574755
PAGE 34 OF 50
3/6/16, 9:32 AM
533574755
Example 5.2 “Readying a wrecking ball”
PAGE 35 OF 50
3/6/16, 9:32 AM
533574755
PAGE 36 OF 50
Example 5.2 “Readying a wrecking ball” according to abe’s variation
(a) Review of tension force “T” in a rope (4 possible tension forces!!)
 Consider a vertically hanging wrecking ball on a rope.
What are the four tension forces associated with the rope?
Make a FBD for the just the wrecking ball. What is the magnitude of the tension force on the
ball? (2500. N)
(b) Let’s redraw the free body diagram for just the ball.
 Write down Newton’s 2nd Law equations for static equilibrium
Note the difference between “force magnitudes” and “force components”
Equation 1
X equation
- T1 + T2 sin + 0 = 0
Equation 2
Y equation
0 + T2 cos + (- 2500. N) = 0
We have 2 simultaneous equations. Solve (8th grade)
T2 = 2.66 x 103 N
T1 = 910. N
3/6/16, 9:32 AM
533574755
PAGE 37 OF 50
Example 5.3
Tension in towing a car at a constant velocity (zero acceleration or
“dynamic equilibrium”) Note: Fnet = 0 even though the car is in moving!!
 Sketch free body diagram
Note force magnitudes (+) T, f, n, Wt
Wt = 1500.· 9.80 = 1.47 x 104 N
Note force components (+) Tx, Ty, fx, fy, nx, ny, Wtx, Wty
#1
X equation
T cos + (- 320. N) + 0 + 0 = 0
#2
Y equation
T sin + 0 + n + (- Wt) = 0
T = 341. N
n = 1.46 x 104 N < Wt
3/6/16, 9:32 AM
533574755
PAGE 38 OF 50
Example 5.5 Tension in towing a car with constant acceleration (not in equilibrium!)
Find the tension T in the rope.
 Draw motion diagram
 Draw free body diagram
Note force magnitudes (+) T, f, n, Wt
Wt = 1500.· 9.80 = 1.47 x 104 N
Note force components (+) Tx, Ty, fx, fy, nx, ny, Wtx, Wty
#1
X equation
find aX = VX / t = 1.20 m/s2
T cos + (- 320. N) + 0 + 0 = M aX
T = 2.26 X 103 N
Note: If you have time, use the Y equation to find the normal force magnitude n.
#2
Y equation
T sin + 0 + n + (- Wt) = M aY
3/6/16, 9:32 AM
533574755
More on Friction Forces
Static friction “model”
PAGE 39 OF 50
fs
fS ≤ fSMax
fSMax = S FN
S = Coefficient of static friction for a “rough” surface
(for a “smooth” frictionless surface, S = 0 )
With “static” friction, the object does not move on the surface.
Note that (for this model) the static MAXIMUM friction force is proportional to the normal force.
o This should be “intuitive.” Let’s demonstrate. Try to move a book on the desk
surface while I push down on the book. The harder I push down on the book, the
harder it is for you to move the book.
 Kinetic friction “model” for sliding friction
fk
fK = K FN
K = Coefficient of kinetic friction for a “rough” surface
(for a “smooth” frictionless surface, K = 0 )
With “kinetic” friction, the object slides on the surface.
Friction force
axis f
Magnitude of friction force f versus magnitude of applied force Fa
Static friction
Kinetic friction
fsmax
Note fK
Fa = fsmax
= K FN = CONSTANT <
Fapplied axis
fSMAX
3/6/16, 9:32 AM
Friction force
axis f
533574755
PAGE 40 OF 50
Magnitude of friction force f versus magnitude of applied force Fa
fS ≤ fSMax
fSMax = S FN
Static friction
Kinetic friction
fsmax
Note fK
Fa = fsmax
= K FN = CONSTANT <
Fapplied axis
fSMAX
3/6/16, 9:32 AM
533574755
Figure 5.17 Static friction keeps an object from slipping
PAGE 41 OF 50
3/6/16, 9:32 AM
533574755
PAGE 42 OF 50
Figure 5.19 The kinetic friction force is opposite to the direction of motion.
3/6/16, 9:32 AM
533574755
PAGE 43 OF 50
A box of books is initially at rest on a floor. The mass of the box is 90.0 kg. The coefficients of static and kinetic friction for the bottom of the box and the floor are
µs = 0.700 and µk = 0.600 . Let the applied force Fapp on the box be horizontal.
(a) On the above figure, sketch and label the remaining forces on the box.
(b) Calculate the magnitude of the normal force.
(c) For the following table, calculate the magnitude of the friction force and state whether the box is moving or not.
Fapplied
Friction Force
Does box move ? If so, what is the acceleration a X?
___________________________________________________________________________________
50 N
___________________________________________________________________________________
100 N
___________________________________________________________________________________
250 N
___________________________________________________________________________________
400 N
___________________________________________________________________________________
600 N
___________________________________________________________________________________
650 N
___________________________________________________________________________________
700 N
___________________________________________________________________________________
A box of mass M = 15.0 kg is motionless on a rough inclined plane at an angle of 35.0 degrees with respect to the horizontal. The coefficient of static friction for
the box and plane is .800. Hint: Use tilted coordinate system for this problem.
(a) Illustrate all forces acting on the box.
(b) On a diagram, show the x and y components of the gravitational force. Also, calculate these components. (84.4 N, -120. N)
(c) Use the equilibrium condition for y-components of force to calculate the magnitude of the normal force.
(d) Calculate the magnitude of the friction force.
(e) If the mass of the box is increased sufficiently, will it start to slide ?
(f) At what angle will the box start to slide?
3/6/16, 9:32 AM
533574755
Two types of forces
PAGE 44 OF 50
continued
 2. Action at a distance forces
force seems to act through “empty space”
o Gravitational force
Fg
Weight = “Wt” = M g
Wt  " weight of object "
o Electric and magnetic forces
Fundamental particles electron, proton, neutron
More fundamental
proton and neutron are composites of quarks
o Nuclear (strong) and nuclear (weak) forces
3/6/16, 9:32 AM
533574755
PAGE 45 OF 50
Newton’s Law of Universal Gravitation
Fundamental Law of Gravity between any two objects in
the universe (includes Solar System and beyond. The force seems to have an infinite range. This is
an exact law with only tiny corrections from General Relativity.
Fon 2 by 1
Fon 1 by 2
M1
M2
r
Fon 1 by 2 = Fon 2 by 1 =
F = G M 1 M2 / r 2
G = 6.67 x 10-11 N m2 / kg2
3/6/16, 9:32 AM
533574755
PAGE 46 OF 50
2
What is the relation between G and g = 9.80 m / s ?
Consider the gravitational force on a basketball at the surface of the Earth.
Fon B by E = MB g
Fon E by B
Mball
MEarth
r = R E + RB
RE
r
RB
r ≈ RE
3/6/16, 9:32 AM
533574755
PAGE 47 OF 50
FEB = FBE = F = G ME MB / r 2
FBE = MB g = F = G ME MB / r 2
M B g = G ME MB
/ RE 2
g = G ME / RE 2
On the surface of the Earth
g = (6.67 x 10-11) (5.98 x 1024) / (6.38 x 106)2
g = 9.80 m / s2 (SI units)
g = 980. cm / s2 (CGS units)
g = 32.2 ft /s2 (BE units)
On the surface of the Moon
gMoon = (6.67 x 10-11) (7.35 x 1022) / (1.74 x 106)2
gMoon = 1.62 m / s2
Memorize:
Newton’s Laws and corresponding formulas; formulas for static and kinetic friction forces.
3/6/16, 9:32 AM
533574755
MORE Optional HOMEWORK PROBLEMS WITH ANSWERS
PAGE 48 OF 50
All SI, BE, and CGS units defined until present assignment.
(1) A constant force of 3.75 N is applied to a hockey puck in the positive x-direction. (Note: A hockey stick remains in contact with the puck in order to apply the
constant force.) The puck is initially at rest at the origin; its mass is .150 kg. Assume there is no friction between the puck and the ice. (a) What is the
acceleration in the x-direction ? (b) At what time t will the puck have a speed of 5.20 m/s ? (c) How far has the puck moved at the time from part (b) ? [HRF3,54E] ( 25.0 m/s2, .208 s, .541 m )
(2) A 200 kg boat is being pulled in the water by two ropes. The first rope exerts a force magnitude F1 of 700. N in the positive x-direction; the second rope
exerts a force magnitude F2 of 900 N at an angle of 30.0 degrees CCL with respect to the positive x-direction. (a) Make a vector diagram which illustrates the two
forces and their resultant force FR . (You may wish to use the “parallelogram rule”.) (b) Calculate the x and y components of FR. (c) Calculate the x and y
components of the acceleration vector of the boat. (d) Calculate the magnitude and angle of the acceleration vector. (e) Assuming the boat starts from rest, find
where its coordinates after 8.00 s and the distance which it has moved. (1.48 . 103 N, 450. N, 7.40 m/s2, 2.25 m/s2, 7.73 m/s2, 16.9 degrees CCL WRT + x
direction, 237.,72.0, 247.)
(3) Given a 5 kg box which is resting on the surface of the earth. (a) Make a free body diagram of the box. Sketch and label all forces which act on the box. (b)
Calculate the magnitude of each force acting on the box. (c) Make a “cartoon” sketch of the box sitting on the earth. Illustrate action and reaction pairs.
(4) Given a 5 kg box which is hanging by a rope. (a) Make a free body diagram of the box. Sketch and label all forces which act on the box. (b) Calculate the
magnitude of each force acting on the box. (c) Sketch the box hanging from the ceiling. Illustrate action and reaction pairs.
(5) A woman is walking on the floor. What is the origin of the force which causes her to move forward? Make a sketch to illustrate.
(6) Calculate the "weight" and "mass" for each of the following. Use SI units for your answer. (a) a "5.00 lb" bag of sugar. (b) a "240 lb" fullback. (c) a "1.80 ton"
automobile. [HRF3,5-15E] (22.2 N, 2.27 kg, 1.07x103 N, 109. kg, 1.60x104 N, 1.63x103 kg)
(7) A man “weighs” 150 lbs. (a) Calculate his weight and mass in SI units. (b) Calculate his weight and mass in BE units. (c) Calculate his weight and mass in
CGS units.
WAIT (8) Sketch and calculate the magnitudes of the tension forces for each of the following ? Let M = 5 kg. Assume frictionless and massless pulleys. (49.0 N,
24.5 N, 24.5 N) Can you design a system which reduces the tension below 15 N. See “Solved Problem 1” in Cutnell and Johnson.
(9) An automobile which weighs 3800 lbs is accelerating at 12.0 ft/s 2 along the positive x-axis. (a) Calculate the mass of the automobile in British units. (b)
Calculate the force on the automobile in British units. (c) What is applying the force to move the automobile? [HRF3,5-20E] (119 slugs, 1.43x103 lbs, to be
discussed in class)
(10.0) Given two boxes stacked on the floor. The top box is 5 kg and the bottom box is 8 kg. Sketch the boxes and show all forces acting on the system. Which
forces are “action & reaction” pairs ? Where do the missing “reaction” forces act ? Make a free-body diagram for the bottom box. Calculate the magnitude of
each force on the bottom box.
(10.1) You are walking on the floor. What is the origin of the force which causes you to move forward? Which of Newton’s three laws applies? Make a sketch to
illustrate your answer.
(11.0) Two railroad cars are being pulled along the positive x-axis by an engine which exerts a force F of magnitude 6500 N. The two cars are connected by a
rope with tension FT . Assume there is no rolling friction. The masses are as follows: M1= 1200 kg and M2 = 2400 kg . Calculate the magnitude “ a” of the
3/6/16, 9:32 AM
533574755
PAGE 49 OF 50
acceleration of the system of the two railroad cars and the tension “F T” in the rope. [HRF3,5-43P] (1.81 m/s2, 4.34 . 103 N) Suggested approach: set up a freebody diagram and free-body equations for each car; get two simultaneous equations in “a” and “F T”.
(11.1) See figure below. Given an Atwood’s machine (two masses hanging on a frictionless pulley). Let M 2 > M1. Show that the magnitude of the acceleration is
given by a = g (M2 - M1)/(M1 + M2) and that the tension in the string is
FT = 2 M1 M2 g/(M1 + M2). Hint: Set up free-body diagrams. What is the relation between a1y , a2y , and a ?
y axis
a
M1
a
FT
M2
FT
M2
x axis
M1
(11.2) See right hand figure above. Given the following simple machine. Let M 1 = 4 kg and M2 = 2 kg. Find the tension in the string and the magnitude of the
acceleration. Assume that M1 slides on a frictionless surface. Hint: Set up free-body diagrams. What is the relation between a1x , a2y , and a ? [HRF3,5-23E]
(13.1 N, 3.27 m/s2)
(11.3) See right hand figure above. Given the following system of two masses. The the surface on which M1 rests has a coefficient of kinetic friction equal to
0.150. Let M1 = 4 kg and M2 = 2 kg. Find the tension in the string and the magnitude of the acceleration of the system. Hint: Set up free-body diagrams and freebody equations. What is the relation between a1x and a , and, between a2y and a ? (15.0 N, 2.29 m/s2) Note: Do not use any formulas from text; start with
free body diagrams and free body equations (Newton’s Second Law) to arrive at answers.
WAIT (11.3) Given the following machine. Let a1 = 6 m/s2. Determine a2. What are the x and y components of a1 and a2 ?
(12) A 160 lb man stands on a bathroom scale in an elevator which is at rest. (a) When the elevator starts moving the scale reads 200 lbs. Find the accleration
(magnitude and direction) of the elevator. (b) The elevator is again at rest. But, when the elevator starts to move this time, the scale reads 120 lbs. Find the
accleration (magnitude and direction) of the elevator. (c) If the scale reads zero, should the man worry? Explain. (+8 ft/s 2, -8 ft/s2, Yes!....) (new)
(13) Given an acrobat of mass M hangs in the middle of a tightrope. Show that the tension in the rope is given by
FT = M g /(2 sin( )) . The angle  is the angle between the horizontal and the rope at the points where it is tied.
(14) Given a 3 kg metal puck which is sliding on ice. The coefficient of kinetic friction between the puck and the ice is 0.0255 . At t = 0 , the speed of the puck is
5 m/s. (a) Sketch all forces on the moving puck. (b) Calculate the magnitude of the force of kinetic friction on the puck. (c) Calculate the x-component of
acceleration. (d) Estimate when the puck will come to rest. (e) How far will the puck have moved? (0.750 N, -.250 m/s2,20.0 s, 50.0 m)
(15) A box of books is initially at rest on a floor. The mass of the box is 80 kg. The coefficients for static and kinetic friction between the bottom of the box and the
floor are 0.750 and 0.650. A horizontal force is applied to the box in the positive x-direction. (a) Sketch the box and show all forces acting on it. (b) Calculate
the magnitude of the force of friction and state whether the box moves for each of the following applied forces: 150 N, 450 N, 575 N, 720 N, 985 N. Hint: Do a
3/6/16, 9:32 AM
533574755
PAGE 50 OF 50
quick calculation with the coefficient of static friction first. (150 N, No; 450 N, No; 575 N, No; 510 N, Yes; 510 N, Yes)
(16) A dockworker loading crates on a ship finds that a 20 kg crate, initially at rest on a rough horizontal surface, requires a 75 N horizontal force to set it in motion.
However, after it is in motion, horizontal force of 60 N is required to keep the crate moving with a constant speed. Find the coefficients of static and kinetic friction
between the crate and the floor. (.383,.306)
(18) To move a box of books along the floor, it is necessary for a rope to have a tension of 80.0 N at an angle of 35.0 degrees. The box of books has a mass of
25.0 kg and the coefficient of kinetic friction between the box and the floor is 0.300. (a) Make a free-body diagram of all the forces acting on the box. On your
diagram, illustrate the x and y components of the tension force of the rope on the box; also, calculate these components. (b) Calculate the normal force on the
box. (c) Calculate the magnitude of the kinetic force of friction on the box. (d) Use Newton's second law to calculate the horizontal acceleration of the box. [SF2,
Example 3.5] (65.5 N,45.9 N,199 N,59.7 N,0.232 m/s2)
(19) A man is applying a horizontal force to drag a 200. kg box of books on a floor whose static and kinetic coefficients of friction are 0.500 and 0.450. The box is
moving with a constant speed of 2 m/s. Calculate the magnitude of the force that the man applies to the box. (882. N) (new)
Given the following object of mass M = 15.0 kg which is hanging from the ceiling as shown.


M
(a) With a free-body diagram, illustrate the tension forces on the knot. Sketch the x and y components of tension forces T1 and T2 on the knot. (b) Apply the
equilibrium condition to the hanging mass in order to calculate the tension T3. (T3 = 147. N) (c) Specify the x and y components of the three tension forces on
the knot in terms of the magnitude of the tension force and, if necessary, the appropriate trigonometric function. (d) Using the equilibrium condition for forces,
write down the two x and y free-body equations for the knot. (e) Solve for the magnitudes of the tensions, T1 and T2 . (T1 = 147. N, T2 = 134. N)
(20) Does the following conversion equation make sense “physically” ? 1 lb = 2.20 kg
units and in terms of exclusively force units.
Explain how it should be corrected to read in terms of exclusively mass