AP Physics 1: Algebra-Based 2 Force and Translational Dynamics Questions

Explain translational motion through system models, force diagrams, Newton’s laws, gravitational and contact forces, springs, and circular motion.

Exam points

choose a system boundary and determine centre-of-mass location, velocity or acceleration
draw a complete free-body diagram and translate its external-force vectors into component equations
identify equal-and-opposite interaction pairs and explain unequal accelerations for different masses
set the vector sum of forces to zero for equilibrium or constant-velocity motion
apply Newton’s second law to connected systems and predict acceleration as force, mass or friction changes
calculate gravitational force or field from mass and distance and combine multiple gravitational vectors
calculate apparent weight under acceleration and distinguish invariant mass from changing weight
calculate kinetic friction, static-friction limits or coefficients from force and motion data
apply Hooke’s law and use force-extension graphs or experiments to determine spring behaviour
resolve real forces into a radial equation and determine circular speed, period or loop-contact limits
analyse tangential and centripetal acceleration together in nonuniform circular motion
derive or apply Kepler’s third law and compare orbital speed or period as radius changes
design force-model experiments from measured mass, motion, force or extension data

Covered syllabus points

2.1 Systems and Center of Mass 2.2 Forces and Free-Body Diagrams 2.3 Newton’s Third Law 2.4 Newton’s First Law 2.5 Newton’s Second Law 2.6 Gravitational Force 2.7 Kinetic and Static Friction 2.8 Spring Forces 2.9 Circular Motion

[Maximum number: 3]

(12 points, suggested time 25 minutes)

(a)

The students calculate the value of $g_{\text {exp }}$ to be significantly lower than the accepted value of $9.8 \mathrm{~m} / \mathrm{s}^{2}$ .

[ 3 ]

(i)

What is a physical reason, other than friction or air resistance, that could lead to a significant difference in the experimentally determined value of $g_{\text {exp }}$ ?

[ 1 ]

(ii)

Briefly explain how the physical reason you identified in part (c)(i) would lead to the decrease in the experimentally determined value of $g_{\text {exp }}$ .

Figure for Question (ii) — AP Physics 1: Algebra-Based

The students want to confirm that the acceleration is the same whether the cart rolls up or down the ramp. The students start the cart at the bottom and give the cart a quick push so that it rolls up the ramp and momentarily comes to rest. The x-axis is still defined to be parallel to the ramp with the origin at the top.

[ 2 ]

For correctly indicating the functional dependence between the reason listed in part (c)(i) and $g_{\text {exp }}$

Accept one of the following:

- Correctly indicating the functional dependence between the physical factor in the materials used and $g_{\text {exp }}$ (e.g., if the rotational inertia of the rotating wheels is nonnegligible, the cart will have a smaller acceleration and $g_{\text {exp }}$ will be smaller.)

- Correctly indicating the functional dependence between the physical factor in the environment and $g_{\text {exp }}$ (e.g., if the experiment was performed at a high elevation, the acceleration will be smaller and $g_{\text {exp }}$ will be smaller.)

- Correctly indicating the functional dependence between the physical error in the measurement collection and $g_{\text {exp }}$ (e.g., if the angle of the ramp is smaller than the measured value, the cart will have a smaller acceleration and $g_{\text {exp }}$ will be smaller.)

Example Response

The expression I derived for the value for $g_{\text {exp }}$ did not take into consideration that the wheels had any rotational inertia. If the wheels have rotational inertia and are rotating, the acceleration of the cart would be less than $g \sin \theta$ , so the value of $g_{\text {exp }}$ would be less than $9.8 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}$ .

Total for part (c) 2 points

[Maximum number: 4]

Figure for Question 2 — AP Physics 1: Algebra-Based

(12 points, suggested time 25 minutes) A student in a physics lab has a block with a fan attached to it, as shown in the figure above. The fan has a pivot so that the angle $\theta$ it makes with the horizontal can be adjusted between 0° and 90°. When the fan is pointed horizontally so that $\theta=0^{\circ}$ , the block accelerates from rest along a track, even though there is friction between the block and the track. For the following questions, assume that the student has access to equipment that would usually be found in a school physics laboratory.

(a)

Describe an experimental procedure that the student could use to measure the force F that the air exerts on the fan-block system when the fan is turned on. Assume that the magnitude of this force is the same for all angles $\theta$ .

[ 3 ]

(a)

i, ii, and iii) 2 points

Note: Parts i, ii, and iii are read together

For measuring the mass or weight of the relevant system

1 point

For making a measurement of force (or something from which a force can be calculated)

1 point

with the fan turned on

Note: fan angles of either 0° or 90° need not be measured directly, since these are

given as the minimum and maximum angles possible. If the procedure involves

intermediate angles, then these angles must be measured.

Example 1 (variant - Example 1a in parentheses):

(a)i The downward force exerted by the fan-block system (or "mass", as read on a

balance, of the system)

(a)ii A spring scale (or mechanical balance)

(a)iii Set the fan angle to 90°. With the fan off, hang the system from a spring scale to

find its weight (or place the system on a mechanical balance to find its mass).

Turn the fan on, and record the force from the spring scale (or the mass reading

from the mechanical balance).

Example 2:

(a)i Mass of the fan-block system and low-friction cart. Velocity of the cart as a

function of time.

(a)ii Scale to measure mass. Motion detector to measure velocity as a function of time.

(a)iii Place the system and a low-friction cart on a scale to find the total mass of the

fan-block and cart. Next, on a horizontal surface, place the fan-block on the cart,

set the fan angle to zero, turn on the fan, and release the cart from rest. Use the

motion detector to graph the cart velocity as a function of time.

iv) 1 point

For correctly indicating a method to determine the force exerted by air on the fan, using

1 point

the measurements and procedure from parts (a) i, ii, and iii

Example 1 (and 1a), continued from above:

Take the difference in the force readings with the fan off and the fan on. (1a:

Multiply the difference in the mass readings by g ). This difference is the force

exerted by air on the fan.

Example 2, continued from above:

Estimate the average slope of the graph, which is the acceleration. Multiply

acceleration by the total mass to find the force exerted by air on the fan.

(i)

What quantities would be measured?

(ii)

What equipment would be used for the measurements, and how would that equipment be used? Include a labeled diagram of the experimental setup.

(iii)

Describe the overall procedure to be used. Give enough detail so that another student could replicate the experiment.

(iv)

Describe how the force can be determined from the measurements described in parts (a)i-iii.

(b)

Describe an experimental procedure that would allow the student to use the fan-block system, with the fan turned on, to find the coefficient of kinetic friction between the block and the track.

[ 3 ]

(i)

On the dot to the right, which represents the fan-block system, draw and label the forces (not components) that are exerted on the system during the experiment described in parts (b)i-iii. Represent each force by a distinct arrow starting on, and pointing away from, the dot.

(c)

Describe how to analyze the data from the experiment described in parts (b)i-iii in order to determine the coefficient of kinetic friction between the block and the track. Your analysis may include the force F exerted by the air on the fan-block system. Do not add to the free-body diagram in part (b)iv.

[ 4 ]

For using kinematic data to obtain acceleration, a, or showing that a=0

Alternatively the point can be earned using the Work-Energy solution with kinetic

energy $K=(1 / 2) m v^{2}$

For relating frictional force and coefficient of kinetic friction as $F_{f}=\mu_{K} F_{N}$

For a correct representation of the normal force, correctly referring back to a

measurement of the fan-block system

$F_{N}=m g$ if $\theta=0$ or $F_{N}=m g+F \sin \theta$ if $\theta \neq 0$

For using Newton's second law, consistently with normal force above, for the

appropriate forces or force components in the direction of the fan's motion that

would lead to the determination of the coefficient of kinetic friction

$F_{\text {net }}=m a$

$F-F_{f}=m a$

$\mu_{k}=\frac{F-m a}{m g}$ if $\theta=0$ or $\mu_{k}=\frac{F \cos \theta-m a}{m g+F \sin \theta}$ if $\theta \neq 0$

Alternatively the point can be earned using the Work-Energy solution that would lead

to the determination of the coefficient of kinetic friction.

Example 3 (continued from above): $\theta=0$ Determine the slope of each v vs. t graph,

to get the acceleration for each trial, and average the accelerations. Call this average

acceleration a. The kinetic frictional force exerted by track on block is

$F_{f}=\mu F_{n}=\mu m g$ , where m is the mass of the fan-block as found in part (a), since

the acceleration is purely horizontal and hence $F_{n}$ and m g must balance. So, by

Newton's second law, letting F denote the force exerted by the air on the fan found

in part (a), we get

Solve for $\mu$ to get $\mu=\frac{F-m a}{m g}$

Example 4 (continued from above): $\theta=0$ Let d denote distance from block to second

photogate and t denote the corresponding time. Since $v_{0}=0, d=\frac{1}{2} a t^{2}$ and

hence $a=\frac{2 d}{t^{2}}$ . For each trial, calculate that acceleration, and take the average,

which becomes our best estimate of a. [Rest of solution is as in example 3]

[Maximum number: 1]

Consider the situation in which your hand is pushing a book across a rough desktop with lots of friction. Of the many forces involved, consider only these two individual forces: the force on your hand from the book and the force the book is experiencing from your hand. While the book is accelerating from rest to its final velocity, which statement best compares the force experienced by your hand compared with that experienced by the book?

Force on book > force on hand

Force on hand > force on book

Force on hand = force on book

The relationship between these two forces depends on the frictional force.

[Maximum number: 1]

Figure for Question 4 — AP Physics 1: Algebra-Based

Three identical blocks, A, B, and C, slide on three dif ferent rough ramps, 1, 2, and 3, respectively. Ramp 3 is steeper than Ramp 2, which is steeper than Ramp 1, as shown. The blocks slide with constant velocities. Which block, if any, experiences the greatest net force?

Block A

Block B

Block C

All blocks experience the same net force.

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question 2

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question (b)

Question (i)

Question (c)

Question 3

Question 4