Name (printed) _______________________________
First Day Stamp
LABETTE
NEWTON’S FIRST LAW OF MOTION - TORQUE
PURPOSE
•
To calculate torques responsible for creating a system with rotational equilibrium.
•
To use Newton’s First Law of Motion, in a system with rotational equilibrium, to calculate an unknown
torque if all other torques in the system are known.
(Note: Throughout this labette we will use the convention of positive torques causing counterclockwise
rotation and negative torques causing clockwise rotation).
PROCEDURE (PART 1)
1.
Insert a meter stick into a balance clamp (figure 11.26) and place onto an iron
“u.” Adjust the position of the clamp until the meter stick balances level on the
iron “u” (figure 11.27). Record the center of mass for the meter stick to the
nearest millimeter.
Figure 11.26: Meter stick
inserted in clamp.
Figure 11.27: Meter stick balanced on iron “u.”
Point of rotation for
meter stick
2.
Place a 20-g mass on a mass hanger and hang on the meter stick near the end of the meter stick. Place a
50-g mass on another mass hanger and hang it on the other side of the meter stick at the spot that balances
the meter stick again.
3.
Record the distance from each of the mass hangers to the point of rotation of the meter stick. These
measurements are the “lever arms.”
DATA
Record masses in kilograms and note that the mass hangers have a mass of 5 grams each. Record distances in meters.
1.
Hanging mass #1
__________ kg
Lever arm #1
__________ meters
2.
Hanging mass #2
__________ kg
Lever arm #2
__________ meters
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QUESTIONS/CALCULATIONS (SHOW ALL WORK)
1.
Each of the hanging masses provides a torque to the meter stick. The torque is the product of the weight of
the hanging mass and the lever arm. (Note that Weight = ( mass)( 9.8 Newtons / kg) and the force will have the
unit of Newtons). Calculate the torque produced by each of hanging masses. Remember that throughout this
lab we are using the convention of positive torques causing counterclockwise rotation and negative torques
causing clockwise rotation. Express these torques in Newton•meters (N•m).
2.
Add the two torques produced by the hanging masses. What does this result imply about the sum of the
torques acting on a system that is in static equilibrium (a system that is not rotating)?
PROCEDURE (PART 2)
1.
Now move the clamp about 10 cm to one side. The meter stick will no longer balance if supported at the
clamp, but if weight is added to the light side, a balance can once again be achieved. Add the two sets of
masses to the light side until the meter stick is balanced again (figure 11.28).
Center of mass of
meter stick
#1
#2
Figure 11.28: Meter stick balanced with two hanging masses on one side. Note the position of the
meter stick’s center of mass.
2.
Measure the distances from the point of rotation to each of the hanging masses and to the center of mass of
the meter stick. These measurements are the “lever arms.”
DATA
1.
Meter stick center of mass __________ meters
Lever arm of center of
__________ meters
mass (the distance you moved the clamp)
2.
Hanging mass #1
__________ kg
Lever arm #1
__________ meters
3.
Hanging mass #2
__________ kg
Lever arm #2
__________ meters
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QUESTIONS/CALCULATIONS (SHOW ALL WORK)
1.
There are now three torques creating rotational equilibrium. On the one side of the point of rotation, there
are two torques due to the weights of the hanging masses. On the other side, the torque comes from the
weight of the meter stick. This weight can be considered to be concentrated at the center of mass.
Calculate the torques produced by the hanging masses.
2.
Using Newton’s First Law of Motion, write an equation making the torques causing counter-clockwise
motion equal to those causing clockwise motion. The unknown torque caused by the meter stick can now be
determined.
3.
Use the torque produced by the meter stick and the lever arm of the meter stick (distance you moved the
clamp) to calculate the force exerted by the meter stick. This will be its weight.
4.
Use the weight of the meter stick and the conversion for mass to weight to calculate the mass of the meter
stick. When you are finished with this part, bring your work and your meter stick to me to be checked.
Predicted mass of meter stick
Actual mass of meter stick
___________ grams
___________ grams
3
5.
The drawing below is meant to represent the lab you just completed. Make length measurements on the
drawing and do calculations like those you did in the lab in order to determine the mass of the stick
supporting the weights.
15 g
25 g
6.
The board below has a mass of 50 g. It balances with the two weights shown. Calculate the mass of the
weight on the right.
10 g
7.
m
The board below has a mass of 5.0 kg. Where would you have to hang an additional 70 N of weight to
balance the board as shown?
8.0 N
8.
The board below has a mass of 1.0 kg. Assume that 30-N weight and a 50-g weight will be hung from the
board, as shown. Calculate where a 2.0kg weight would need to be placed for the board to balance.
30 N
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50 g
QUESTIONS AND PROBLEMS
STATIC EQUILIBRIUM
Do the following problems from the Giancoli book in the space provided below and on the following page.
Pages 246 – 252, Question 8; Problems 2, 13, 16, 57, 68a
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LAB
NEWTON’S SECOND LAW OF MOTION
INTRODUCTION
Try accelerating in a car; first downhill, then on
level ground, and then uphill. You get a different
experience each time. When you accelerate uphill or
downhill you have at least three forces acting on you:
1. the force from the engine (helping you to
accelerate)
2. the force of gravity pulling you downhill
(helping to accelerate you when you go
downhill and acting against you when you go
uphill)
3. the force of air resistance (always acting
against you)
When you accelerate on level ground, you lose the
force of gravity’s effect on the acceleration. The
point here is that each case involves multiple forces
(not all acting in the same direction) producing
different accelerations. Newton’s Second Law of
Motion is far more powerful than being limited to
accelerations involving only a single force though.
(Good thing since most acceleration involves
multiple forces.) This lab brings you along a bit
further, asking you to consider the non-trivial case of
not only multiple forces but also the mass being
distributed in more than one place.
PURPOSE
•
To become familiar with the dynamics carts, tracks, and photogate timing systems as well as their use in
investigating motion.
•
To investigate the relationship between the mass of an object or objects, the force(s) acting on it (them), and
the resulting acceleration.
Figure 11.29: Ariel Berman (left, Class of 2007) releases a dynamics cart that accelerates along a dynamics track
toward Sasha Novis (Class of 2006). The cart accelerates due to the weight of a hanging mass, which is suspended
over a Super Pulley and attached by string to the cart. The time for the run is recorded by an electronic photogate
system. A mass hanger attached to the top of the cart acts as a flag to start and stop the timer. Sasha is poised to
stop the run before the cart reaches the end of the track.
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PART 1A
You will use a dynamics cart (500 g), friction block and flag as mass m1 on a horizontal track with a string
attached over a pulley to a mass m2 (Figure 11.30). The net force, F, on the entire system (cart and hanging mass) is
the weight of the hanging mass, assuming that friction is negligible. To obtain the acceleration, the cart will be
started from rest and the time, t, it takes it to travel a certain distance, d, will be measured. Then d = v i t + 12 at 2 can
be used to calculate the acceleration.
m1
pulley
cart
track
photogate
timer
end stop
photogate
mass
hanger
Figure 11.30: Experimental setup for Newton’s Second Law
m2
PROCEDURE
1.
Set up the cart with the friction block inserted.
2.
Tape a mass hanger on top of the friction block as a flag to trigger the photogates.
3.
Assume you were to put 200 grams on the mass hanger (5 grams) hanging off the pulley. Use Newton’s
Second Law to predict what the acceleration of the cart should be. Identify and itemize each of the various
masses used in determining your prediction.
Prediction
4.
When you have checked your prediction with me, place 200 grams on the hanging mass hanger and
measure the time required for the cart to move through the two photogates. Use the instructions on the
following page to teach you how to use the photogates
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Measuring time with the photogate timing system
To measure the time:
• Pull the cart back until it touches the rubber
end stop on the dynamics track. This will
be the release point for the cart for the
entire lab.
• Move the photogate timer back to the cart
so that the flag on the cart will
immediately trigger the timer when the
cart is released (Figure 11.31). This allows
for the initial velocity of the cart to be very
close to zero.
• Place the other photogate about 80 cm
away from the photogate timer, measure
Figure 11.31: Cart readied for release.
the distance between photogates, and
record it.
• Pull the cart back to the rubber
end stop and hold it there.
• Set the photogate timer to Pulse
Mode, which measures the time
Pulse
between gates (Figure 11.32).
mode
• Set the photogate timer to the
setting
1-ms setting (Figure 11.32).
Time
Otherwise, the maximum time
incre
increment that it measures is 2.0
seconds.
• Check the length of the string. It
should be short enough that the
mass hanger hits the ground after
the flag passes the second timer.
It should be long enough that the
mass hanger hits the ground
before the cart reaches the end of
Figure 11.32: Photogate timer settings
Memory
the track.
“ON”
• Release the cart and record the
time. Repeat at least four more times (until the spread of times is less than 1%). Have the partner who is
not releasing the cart stop the cart after it passes through the second photogate and before it hits the end
of the track. Also, put some sort of cushion underneath the mass hanger so that it doesn’t strike the floor
directly.
DATA
1.
Distance between photogates: ___________
Time (s)
2.
Average time for cart: ___________
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QUESTIONS/CALCULATIONS (SHOW ALL WORK)
1.
Calculate the actual acceleration using your distance and time data.
2.
Calculate the percent error.
3.
Carefully account for the discrepancy between the predicted and the actual accelerations. (This not about
saying, “There was experimental error.” If your actual acceleration is lower than you predicted, then your
reasons for discrepancies should be different than if your prediction is higher than predicted.)
4.
How much time would it take the cart to move through the photogates if the mass on the mass hanger were
doubled?
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PART 1B
PROCEDURE
1.
Take 50 grams off the mass hanger and tape it onto the friction block.
2.
Assume you were to release the remaining mass on the hanger hanging off the pulley. Use Newton’s
Second Law to predict what the acceleration of the cart should be now.
Prediction
3.
When you have checked your prediction with me, release the remaining mass on the hanging mass hanger
and measure the time required for the cart to move through the two photogates.
DATA
1.
Distance between photogates: ___________
Time (s)
2.
Average time for cart: ___________
QUESTIONS/CALCULATIONS (SHOW ALL WORK)
1.
Calculate the actual acceleration using your distance and time data.
2.
Calculate the percent error.
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PART 2
BACKGROUND
Part 1 of this lab was designed to help you learn to use equipment that has the potential to allow for excellent
precision and accuracy. While you may not have been able to prove Newton’s Second Law within 1% of your
prediction in Part 1, after thinking about how you conducted that first experiment, hopefully you improved your
precision and accuracy. At this point, you know that Newton’s Second Law is valid and you’ve had some practice
perfecting your technique in using the equipment. Now it’s time to use the equipment and Newton’s Second Law of
Motion to calculate an unknown mass.
PROCEDURE
I will give you an object with an unknown mass. Your goal is to design an experiment using that object, along
with the equipment you used in Part 1 of the lab, to calculate the mass of the object. Use the space below to describe
and diagram your plan. Then provide data and calculations that lead to your predicted mass for the object.
Description of plan:
Diagram of plan:
Data Table:
Calculations:
Experimentally Determined Mass: ____________
Actual Mass: ____________
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QUESTIONS AND PROBLEMS
FREE BODY DIAGRAMS
Free body diagrams are used to represent situations where forces are present
and can be analyzed with Newton’s 2nd Law. The need to identify, draw, and label
a variety of forces is essential (these will be the “givens” for Newton’s 2nd Law
problems). Use the list of forces on the right to label force vectors in the free body
diagrams you make. Details about these forces, like the difference between static
and kinetic friction, will be described later. For now, you are only drawing and
labeling forces.
PROCEDURE
Common Forces
Fg = force of gravity (weight)
Fn = normal force (support)
Fr = air resistance (drag)
Fs = static friction
Fk = kinetic friction
Ft = tension
Fs = spring force
• Draw forces on the dot, to the right of each picture.
• Draw forces with a ruler, and put an arrow on each, to show direction.
• Draw forces that are proportionally correct. That is, if you intend to show equilibrium, then forces are
balanced. If not, then the net force must be in the direction of acceleration.
• Label each force according to the Common Forces list.
• Add an acceleration vector to the side.
• Indicate the direction that will be defined as positive.
1
2
3
4
5
6
13
7
8
9
10
11
12
13
14
15
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QUESTIONS AND PROBLEMS
NEWTON’S SECOND LAW OF MOTION
Do the following problems from the Giancoli book in the space provided below and on the following page.
Pages 98 – 105
Problems 7, 9, 10, 12, 20, 25, 86
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QUESTIONS AND PROBLEMS
NEWTON’S THIRD LAW OF MOTION
1.
a. A small car and large truck have a head-on collision. Which one receives the greater applied force?
Why?
b. Which one has the greater acceleration? Why?
2.
For each of the following “action” forces, identify the reaction force and what effects both the action and
reaction forces cause.
a. A bat applies a force to a baseball.
Reaction force:
Action force effect:
Reaction force effect:
b. A sprinter begins her race by applying a force with her foot backward on the ground.
Reaction force:
Action force effect:
Reaction force effect:
c. A car comes to a rapid stop by skidding its tires forward on the ground.
Reaction force:
Action force effect:
Reaction force effect:
d. A raindrop falls from the sky because the gravitational force of the Earth pulls downward on it.
Reaction force:
Action force effect:
Reaction force effect:
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