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

(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.

(b)

i, ii, and iii) 2 points

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

Note: In parts (b) i, ii, and iii, it is acceptable to say "the same as in part (a), with the

following changes:", with changes to the procedure in part (a) then listed.

For describing measurements that would allow determination of the acceleration

For describing a procedure that is practical/feasible in a school laboratory

Example 3:

Place the fan-block on the track, with angle =0. Place a motion detector behind it,

set to graph velocity vs. time. Turn fan on, and release from rest. Repeat the

procedure several times.

Example 4:

Place the fan-block on the track, with angle =0. Place a photogate just in front of

the block, and the second photogate a meter or two in front of the block. Measure

distance from front of block to the front of that second photogate. Turn on fan and

release the block from rest. The photogates measure the time it takes the block to

travel the measured distance to the second photogate.

Example 5:

(b)i Angle of the fan. Velocity of fan-block system as a function of time.

(b)ii Protractor to measure the angle.

Motion detector to measure the velocity and time.

(b)iii Adjust the fan angle until the fan-block slides with a constant speed after

being given a push. Use the motion detector to determine whether the speed is

constant (zero slope on a graph of velocity as a function of time).

iv) 1 point

For correctly drawn and labeled vectors for the force exerted by air on fan and for the

frictional force exerted on the block by the track, corresponding to the experiment

described in part (b)iii. Other forces correctly drawn and labeled AND no incorrect

forces, corresponding to the experiment described in part (b)iii.

(c) 4 points

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]