APY1 Review
Forces
BIG IDEA 1: Objects and systems have properties such as mass and charge. Systems may have internal structure.
1.C.1.1: The student is able to design an experiment for collecting data to determine the relationship between the net force
exerted on an object its inertial mass and its acceleration. [SP 4.2]
1.C.3.1: The student is able to design a plan for collecting data to measure gravitational mass and to measure inertial mass and to
distinguish between the two experiments. [SP 4.2]
BIG IDEA 2: Fields existing in space can be used to explain interactions.
⃗ = mg
2.B.1.1: The student is able to apply F
⃗ to calculate the gravitational force on an object with mass m in a gravitational field
of strength g in the context of the effects of a net force on objects and systems. [SP 2.2, 7.2]
BIG IDEA 3: The interactions of an object with other objects can be described by forces.
3.A.2.1: The student is able to represent forces in diagrams or mathematically using appropriately labeled vectors with
magnitude, direction, and units during the analysis of a situation. [SP 1.1]
3.A.3.1: The student is able to analyze a scenario and make claims (develop arguments, justify assertions) about the forces
exerted on an object by other objects for different types of forces or components of forces. [SP 6.4, 7.2]
3.A.3.2: The student is able to challenge a claim that an object can exert a force on itself. [SP 6.1]
3.A.3.3: The student is able to describe a force as an interaction between two objects and identify both objects for any force.
[SP 1.4]
3.A.4.1: The student is able to construct explanations of physical situations involving the interaction of bodies using Newton’s
third law and the representation of action-reaction pairs of forces. [SP 1.4, 6.2]
3.A.4.2: The student is able to use Newton’s third law to make claims and predictions about the action-reaction pairs of forces
when two objects interact. [SP 6.4, 7.2]
3.A.4.3: The student is able to analyze situations involving interactions among several objects by using free-body diagrams that
include the application of Newton’s third law to identify forces. [SP 1.4]
3.B.1.1: The student is able to predict the motion of an object subject to forces exerted by several objects using an application
of Newton’s second law in a variety of physical situations with acceleration in one dimension. [SP 6.4, 7.2]
3.B.1.2: The student is able to design a plan to collect and analyze data for motion (static, constant, or accelerating) from force
measurements and carry out an analysis to determine the relationship between the net force and the vector sum of the
individual forces. [SP 4.2, 5.1]
3.B.1.3: The student is able to reexpress a free-body diagram representation into a mathematical representation and solve the
mathematical representation for the acceleration of the object. [SP 1.5, 2.2]
3.B.2.1: The student is able to create and use free-body diagrams to analyze physical situations to solve problems with motion
qualitatively and quantitatively. [SP 1.1, 1.4, 2.2]
3.C.4.1: The student is able to make claims about various contact forces between objects based on the microscopic cause of
those forces. [SP 6.1]
3.C.4.2: The student is able to explain contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic
electric forces and that they therefore have certain directions. [SP 6.2]
BIG IDEA 4: Interactions between systems can result in changes in those systems.
4.A.1.1 The student is able to use representations of the center of mass of an isolated two-object system to analyze the motion of
the system qualitatively and semiquantitatively. [SP 1.2, 1.4, 2.3, 6.4]
4.A.2.1: The student is able to make predictions about the motion of a system based on the fact that acceleration is equal to the
change in velocity per unit time, and velocity is equal to the change in position per unit time. [SP 6.4]
4.A.2.2: The student is able to evaluate using given data whether all the forces on a system or whether all the parts of a system have
been identified. [SP 5.3]
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4.A.2.3: The student is able to create mathematical models and analyze graphical relationships for acceleration, velocity, and
position of the center of mass of a system and use them to calculate properties of the motion of the center of mass of a system. [SP
1.4, 2.2]
4.A.3.1: The student is able to apply Newton’s second law to systems to calculate the change in the center-of-mass velocity when an
external force is exerted on the system. [SP 2.2]
4.A.3.2: The student is able to use visual or mathematical representations of the forces between objects in a system to predict
whether or not there will be a change in the center-of-mass velocity of that system. [SP 1.4]
Inertia and the First Law





Inertia means that matter stays in a state of rest if it it is currently at rest and it says in a state
of constant speed in a straight line if moving.
The measure of inertia is mass. This is called the inertial mass.
The more massive an object is, the more inertia it has.
The statement of the first law: an object at rest will remain at rest, or if it in uniform motion
(constant speed in a strait line), it will continue as such unless acted upon by a net
(unbalanced) force.
A force must be present to cause an object to deviate form its state of either rest or uniform
motion.
Contact Force:



Two forces that are actually touching
Normal Force (Fn) force between two objects that acts perpendicular to that surface
Frictional Force (Ff) the force exerted between two surfaces that act parallel to the surface. It
always points opposite the direction of motion.
𝑭𝒇 ≤ 𝝁𝑭𝒏



 is the coefficient of friction: describe the surface of the material
There are two types of frictional forces: static and kinetic
Tension Force (Ft) force exerted by ropes or does attached to objects.
Spring Force (Fs) this is the force a spring exerts on a body. It always points towards the
equilibrium position.
Fs = kx
Non-Contact Forces:
 Are interactions between two systems that aren’t actually touching
 Force of Gravity: (Fg): Gravitational attraction between Earth and an object near its surface.
Also known as weight. (An object Fg changes as you go to another planet—an object’s mass
does not)
Fg = mg

Gravitational Attraction (Fa) This the attraction between two massive objects
𝑭𝒂 =
𝑮𝒎𝟏 𝒎𝟐
𝒓𝟐
2

Electrostatic Force (Fe): attraction between two charged particles
𝑭𝒆 =
𝒌𝒒𝟏 𝒒𝟐
𝒓𝟐
Action and Reaction and the Third Law


When an interaction takes place between two systems, each system exerts a force on the
other, and these two forces are equal in magnitude and opposite in direction.
You push on nose---nose pushes on you.
Newton’s Second Law

The net force acting on an object is equal to the mass times acceleration.
F = ma
Problem Solving Hints:
1. Draw a free body diagram
2. Write out the Fx and the Fy
3. Use these two equations to find you unknowns.
Free Body Diagrams
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Free Body diagrams are pictorial representations of the forces acing on a body.
The object becomes a dot placed at the origin of your free body diagram.
The forces are drawn from the center of the free body diagram.
The length of the forces should represent the magnitude of the force.
Inclines:

When an object is on an incline, you will shift the free body diagram to make your life easier.
Fn
Ff
Fn
Ff


Fg

Fg
The angle  is always with respect to the y-axis
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Pulleys
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

Pulleys are frictionless and add no inertia to the system.
Their purpose is to serve as agents that redirect forces
without affecting the dynamics of the system.
Remember: Assign direction----the forces is the same, but
acceleration will be in different directions
Statics
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Static is the study of systems in equilibrium.
There are two types of equilibrium: translation and rotational
For an object to be in equilibrium the F must be zero.
This can be accomplished by an object at rest or an object moving with constant velocity.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. A 50-kg student stands on a scale in an elevator. At the instant the elevator has a downward acceleration of 1.0 m/s 2 and
an upward velocity of 3.0 m/s, the scale reads approximately
a. 350 N
b. 450 N
c. 500 N
____
d. 550 N
2. A 6.0 kg block initially at rest is pushed against a wall by a 100 N force as shown. The
coefficient of kinetic friction is 0.30 while the coefficient of static friction is 0.50.
What is true of the friction acting on the block after a time of 1 second?
a. Static friction acts upward on the
b.
____
block.
Kinetic friction acts upward on the
block
c. Kinetic friction acts downward on the
d.
block.
Static friction acts downward on the
block.
3. A student pulls a wooden box along a rough horizontal floor at constant speed by means of
a force P as shown to the right. Which of the following must be true?
a. P > f and N < W. b. P > f and N = W. c. P = f and N > W. d. P = f and N = W.
____
4. A block of mass 3 kg, initially at rest, is pulled along a frictionless,
horizontal surface with a force shown as a function of time t by the graph
above. The acceleration of the block at t = 2 s is
a. 4/3 m/s2
b. 2 m/s2
c. 8 m/s2
d. 12 m/s2
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____
5. The 10.0 kg box shown in the figure to the right is sliding to the right along the
floor. A horizontal force of 10.0 N is being applied to the right. The coefficient
of kinetic friction between the box and the floor is 0.20. The box is moving with:
a. acceleration to the left.
b. acceleration to the right.
____
c. constant speed and constant velocity.
d. constant speed but not constant velocity.
6. A plane 5 meters in length is inclined at an angle of 37°, as shown above. A
block of weight 20 N is placed at the top of the plane and allowed to slide down.
The magnitude of the normal force exerted on the block by the plane is
a. greater than 20 N
c. equal to 20 N
greater
than
zero
but
less
than
20
N
b.
d. zero
____
7. The frictional force on the block exerted by the surface has magnitude f.
What is the acceleration of the block?
a. F/m
____
b. (Fcos)/m
c. (F–f)/m
d. (Fcos–f)/m
8. Each of the diagrams below represents two weights connected by a massless string which passes over a massless,
frictionless pulley. In which diagram will the magnitude of the acceleration be the largest?
a.
____
b.
c.
d.
9. A rope of negligible mass supports a block that weighs 30 N, as shown above. The breaking strength
of the rope is 50 N. The largest acceleration that can be given to the block by pulling up on it with
the rope without breaking the rope is most nearly
a. 6.10 m/s2
b. 10 m/s2
c. 16.7 m/s2
d. 26.7 m/s2
____ 10. When an object of weight W is suspended from the center of a
massless string as shown above, the tension at any point in the
string is
a. 2Wcos
b. ½Wcos
c. W/(2cos) d. W/(cos)
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Experimental Question
Mech 1.
Experiment 1: A block of mass 1.5 kg is placed on a long board. You are to design an experiment to
determine the coefficient of static friction between the block and the board.
(a)
i. From the following list of available equipment, check those additional items you would use for the
purpose of
determining the
coefficient of static
friction.
ii. Sketch a diagram of your experimental setup and label the pieces of equipment that would be used.
iii. Outline the experimental procedure you would use, including a list of quantities you would measure.
For each quantity, identify the equipment you would use to make the measurement.
(b) Explain how to use the measurements described in part (a) to calculate the coefficient of static
friction. Include a free-body diagram in your explanation that shows all forces (not components) acting on
the block while the measurements are being made.
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Experiment 2: In a second experiment, the coefficient of kinetic friction between the block and the board
is determined to be 0.10. The board is now inclined at an angle of 25ᵒ above the horizontal. The block is
released from rest at the top of the incline and slides 2 down the incline.
(c) The mass of the block is now increased without changing the coefficient of kinetic friction, and
experiment 2 is repeated. How does each of the following change? Explain
i. The magnitude of the frictional force
_____Increases
_____Decreases ______Remains the same
ii. The magnitude of the velocity of the block as it reaches the bottom of the incline
_____Increases
_____Decreases ______Remains the same
iii. The kinetic energy of the block at the bottom of the incline
_____Increases
_____Decreases ______Remains the same
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Short Answer
A child pulls a 15 kg sled containing a 5.0 kg dog along a straight path on a horizontal surface. He exerts a force of
55 N on the sled at an angle of 20ᵒ above the horizontal, as shown in the figure above. The coefficient of friction
between the sled and the surface is 0.22.
(a) On the dot below that represents the sled-dog
system, draw and label a free-body diagram
for the system as it is pulled along the surface.
(b) Write two equations that relate your free body diagram to the mass of the dog-sled system and the
acceleration of the dog-sled system.
(c) Qualitatively discuss what happens to the normal force as the angle, θ, is increased or decreased. Calculate
the normal force acting on the dog-sled system.
(d) At some later time, the dog rolls off the side of the sled. The child continues to pull with the same force. On
the axes below, sketch a graph of speed v versus time t for the sled. Include both the sled’s travel with and
without the dog on the sled. Clearly indicate with the symbol tr the time at which the dog rolls off.
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Qualitative/Quantitate
2012 B1
Block A of mass 2.0 kg is pulled along a horizontal table by a
force of 15 N, which is applied by a light string that passes over
a light frictionless pulley, as shown above. The coefficient of
kinetic friction between the block and the surface is 0.25.
(a)
On the dot below, which represents the block, draw
and label the forces (not components) that act on the block as it is pulled across the table.
(b)
Calculate the magnitude of the acceleration of the block.
The applied force is removed. Block B of mass 1.5 kg is now attached to the
string, as shown above. The system is released from rest so that the 1.5 kg
box descends and the 2.0 kg block is again pulled across the table.
(c) Calculate the acceleration of the 1.5 kg block as it descends.
(d) Calculate the tension in the string connecting the two blocks.
(e) Calculate the distance that the 1.5 kg block descends in 0.40 s.
(f) If this system is set up in a laboratory and the acceleration of the 1.5 kg block is experimentally
determined, the experimental value is found to be smaller than the value calculated above. If the
given value for the coefficient of friction is correct and air resistance is negligible, explain briefly, but
specifically, why the experimental value of the acceleration is smaller.
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Paragraph
B3-SCT78: HANGING M ASS—TENSION IN THREE STRINGS
A hanging mass is suspended midway between two walls.
The string attached to the left wall is horizontal while the string
attached to the right wall makes an angle with the horizontal as
shown. This angle () in Case A is larger than the angle () in
Case B. Four students make the following claims about the
tensions in the strings:
Abbie: “I think the tensions in any string in Case A is
going to be the same as the equivalent string
in Case B. The weight is the same, and the weight is still going to be divided up among the three
ropes.”
Bobby: “I think the tensions in the horizontal and vertical strings are the same, because they are exactly the
same in both cases. But in Case B the diagonal rope is shorter, so the tension is more concentrated
there.”
Che: “The diagonal string still has to hold the weight up by itself, because the horizontal string can’t lift
anything. So the diagonal string still has the same tension. But in Case B it’s pulling harder against
the horizontal string because of the angle, so the tension in the horizontal string has to go up.”
Damian: “But the diagonal string is fighting harder against the weight in Case A—it is pointing more
nearly opposite the weight. So it has to have a greater tension in Case A. And since the tension in
the diagonal string is greater, and the tension in the vertical string is the same, the tension in the
horizontal string must be less in Case A. The tensions still have to balance out so that they are the
same in both cases.”
With which, if any, of these students do you agree?
Abbie _____ Bobby _____ Che _____ Damian _____ None of them_____
Write a paragraph that explain your reasoning.
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APY1 Forces Review Session 2015
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
B
C
A
A
A
B
D
A
A
D
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
1
1
1
1
1
1
1
1
1
1
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