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® Physics 1:  
Algebra-Based
Scoring Guidelines

© 2019 The College Board. College Board, Advanced Placement, AP, AP Central, and the acorn logo are 
registered trademarks of the College Board. Visit the College Board on the web: collegeboard.org.

AP Central is the official online home for the AP Program: apcentral.collegeboard.org.

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© 2019 The College Board.  
Visit the College Board on the web: collegeboard.org.

General Notes About 2019 AP Physics Scoring Guidelines 
 
1. The solutions contain the most common method of solving the free-response questions and the allocation of 
points for this solution. Some also contain a common alternate solution. Other methods of solution also 
receive appropriate credit for correct work. 
 
2. The requirements that have been established for the paragraph-length response in Physics 1 and Physics 2 can 
be found on AP Central at  
https://secure-media.collegeboard.org/digitalServices/pdf/ap/paragraph-length-response.pdf.

3. Generally, double penalty for errors is avoided. For example, if an incorrect answer to part (a) is correctly 
substituted into an otherwise correct solution to part (b), full credit will usually be awarded. One exception to 
this may be cases when the numerical answer to a later part should be easily recognized as wrong, e.g., a 
speed faster than the speed of light in vacuum. 
 
4. Implicit statements of concepts normally receive credit. For example, if use of the equation expressing a 
particular concept is worth 1 point, and a student’s solution embeds the application of that equation to the 
problem in other work, the point is still awarded. However, when students are asked to derive an expression, 
it is normally expected that they will begin by writing one or more fundamental equations, such as those 
given on the exam equation sheet. For a description of the use of such terms as “derive” and “calculate” on 
the exams, and what is expected for each, see “The Free-Response Sections  Student Presentation” in the 
AP Physics; Physics C: Mechanics, Physics C: Electricity and Magnetism Course Description or “Terms 
Defined” in the AP Physics 1: Algebra-Based Course and Exam Description and the AP Physics 2: Algebra-
Based Course and Exam Description.

5. The scoring guidelines typically show numerical results using the value 
2
9.8 m s
g =
, but the use of

2
10 m s  is of course also acceptable. Solutions usually show numerical answers using both values when they 
are significantly different. 
 
6. Strict rules regarding significant digits are usually not applied to numerical answers. However, in some cases 
answers containing too many digits may be penalized. In general, two to four significant digits are acceptable. 
Numerical answers that differ from the published answer due to differences in rounding throughout the 
question typically receive full credit. Exceptions to these guidelines usually occur when rounding makes a 
difference in obtaining a reasonable answer. For example, suppose a solution requires subtracting two 
numbers that should have five significant figures and that differ starting with the fourth digit (e.g., 20.295 and 
20.278). Rounding to three digits will lose the accuracy required to determine the difference in the numbers, 
and some credit may be lost.

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Identical blocks 1 and 2 are placed on a horizontal surface at points A and E, respectively, as shown. The 
surface is frictionless except for the region between points C and D, where the surface is rough. Beginning at 
time At , block 1 is pushed with a constant horizontal force from point A to point B by a mechanical plunger. 
Upon reaching point B, block 1 loses contact with the plunger and continues moving to the right along the 
horizontal surface toward block 2. Block 1 collides with and sticks to block 2 at point E, after which the two-
block system continues moving across the surface, eventually passing point F.

(a)
LO 4.A.1.1, SP 1.2, 1.4, 2.3, 6.4; LO 4.A.2.3, SP 1.4, 2.2; LO 4.A.3.2, SP 1.4; LO 5.D.3.1, SP 6.4
5 points

On the axes below, sketch the speed of the center of mass of the two-block system as a function of  
time, from time At  until the blocks pass point F at time Ft . The times at which block 1 reaches points A  
through F are indicated on the time axis.

For a straight line that begins at zero at At  and increases between At  and Bt
 
1 point

For a segment that is horizontal and nonzero between Bt  and Ct
 
1 point

For a segment that decreases linearly between Ct  and D
t   
 
1 point

For a segment that is horizontal, nonzero, and constant (but different value than segment 
from Bt  to Ct ) from D
t  through Ft  (with no change at Et ) 
 
1 point

For a curve that is continuous from At  through Ft , with the possible exception of Et .  
Note: If the speed changes at Et , the fourth point is not earned while this point may still

Note: No credit is earned for a horizontal line along the t-axis.

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Question 1 (continued) 
 
(b)  
LO 4.D.1.1, SP 1.2, 1.4; LO 4.D.2.1, SP 1.2, 1.4; LO 5.E.1.1, SP 6.4, 7.2 
 
 
2 points

The plunger is returned to its original position, and both blocks are removed. A uniform solid sphere is placed 
at point A, as shown. The sphere is pushed by the plunger from point A to point B with a constant horizontal 
force that is directed toward the sphere’s center of mass. The sphere loses contact with the plunger at point B 
and continues moving across the horizontal surface toward point E. In which interval(s), if any, does the 
sphere’s angular momentum about its center of mass change? Check all that apply.

____ A to B          ____ B to C          ____ C to D          ____ D to E 
_____ None

Briefly explain your reasoning. 
 
Correct Answer: “C to D”

For reasoning that a change in angular momentum is caused by a net external torque  
 
1 point

For correctly indicating that friction from C to D is the only force producing an external 
torque over the entire interval from A to E 
Note: This point is not earned if a statement is made that the angular momentum or

angular speed decreases between C and D or that the sphere stops rotating at  
point D.

Claim: The sphere’s angular momentum about its center of mass changes in the  
interval C to D. 
Evidence: There is friction between points C and D.  
Reasoning: Friction applies a torque in region C to D about the central axis of the 
cylinder to increase/change its angular momentum.

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Learning Objectives 
 
LO 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. [See Science Practices 1.2, 1.4, 2.3, 
6.4]  
LO 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. [See Science Practices 1.4, 2.2] 
LO 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. [See 
Science Practice 1.4] 
LO 4.D.1.1: The student is able to describe a representation and use it to analyze a situation in which several 
forces exerted on a rotating system of rigidly connected objects change the angular velocity and angular 
momentum of the system. [See Science Practices 1.2, 1.4] 
LO 4.D.2.1: The student is able to describe a model of a rotational system and use that model to analyze a 
situation in which angular momentum changes due to interaction with other objects or systems. [See Science 
Practices 1.2, 1.4] 
LO 5.D.3.1: The student is able to predict the velocity of the center of mass of a system when there is no 
interaction outside of the system but there is an interaction within the system (i.e., the student simply 
recognizes that interactions within a system do not affect the center of mass motion of the system and is able 
to determine that there is no external force). [See Science Practice 6.4] 
LO 5.E.1.1: The student is able to make qualitative predictions about the angular momentum of a system for a 
situation in which there is no net external torque. [See Science Practices 6.4, 7.2]

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This problem explores how the relative masses of two blocks affect the acceleration of the blocks. Block A, of 
mass 
A
m , rests on a horizontal tabletop. There is negligible friction between block A and the tabletop. Block 
B, of mass 
B
m , hangs from a light string that runs over a pulley and attaches to block A, as shown above. The 
pulley has negligible mass and spins with negligible friction about its axle. The blocks are released from rest. 
 
(a)  
LO 3.A.1.1, SP 1.5; LO 3.B.1.1, SP 6.4, 7.2 
 
 
i. 
 
 
 
2 points 
 
Suppose the mass of block A is much greater than the mass of block B. Estimate the magnitude of the

acceleration of the blocks after release.

Briefly explain your reasoning without deriving or using equations.

Examples of correct answers: “Zero”, “small”, “negligible”, “much less than g”, or 
“<<g”

For a correct answer and attempt at a consistent justification   
 
1 point

Example earning 1 point: 
Nearly zero. Because block A is much heavier than block B.

Examples earning 2 points:  
 “Very small. Because block A has a large inertia, it won’t speed up much.”  
“Close to zero because block B is so light that it can hardly budge block A.”

Claim: The acceleration of the blocks is zero/small/negligible/ “<<g”. 
Evidence: The mass of block A is much greater than the mass of block B.  
Reasoning: See two-point examples above.

ii. 
 
 
 
1 point 
 
Now suppose the mass of block A is much less than the mass of block B. Estimate the magnitude of the

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Question 2 (continued) 
 
(a) (continued) 
 
ii. (continued)    
 
Examples of correct answers: g or 9.8 m/s2 or 10 m/s2 (or just 9.8 or 10)

For a correct answer and correct justification 
 
1 point

Examples: 
Nearly equal to g. Because block B is almost in free fall.  
10 m/s2, because block A has negligible mass and the tension in the string is nearly zero.

Claim: The acceleration of the blocks is close to g. 
Evidence: 
The mass of block A is much less than the mass of block B. 
There is negligible friction between block A and the tabletop.  
The pulley has negligible mass and spins with negligible friction about its axle. 
Reasoning: See examples above.

(b)  
LO 3.A.2.1, SP 1.1; LO 3.A.3.1, SP 6.4 
 
 
3 points 
 
Now suppose neither block’s mass is much greater than the other, but that they are not necessarily equal. 
The dots below represent block A and block B, as indicated by the labels. On each dot, draw and label the 
forces (not components) exerted on that block after release. Represent each force by a distinct arrow 
starting on, and pointing away from, the dot.

For a correct normal force on block A with acceptable label: N, 
N
F , “normal force,”

table
F
, “table force,” or any other label indicating the force is “normal” or comes 
from the table

For correct gravitational forces with acceptable label on both diagrams: 
g
F , 
grav
F
, W,

mg , 
A
m g , “gravity,” “grav force,” but NOT G or g, and no extraneous forces on 
either diagram

For correct tension forces with acceptable label on both diagrams: “tension,” “string 
force,” 
tension
string
, 
, 
, 
, ,
T
S
F
F
F
F
T  or some other label indicating that the force

comes from the string or from tension. NOT acceptable: 
, 
,
m
B
B
m g F
 “force from

block B” or other indications that the force is “created” by block B

Block A                                           Block B

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Question 2 (continued) 
 
(c)  
LO 2.B.1.1, SP 2.2; LO 3.A.1.1, SP 1.5, 2.2; LO 3.B.1.3, SP 1.5, 2.2; LO 3.B.2.1, SP 1.4, 2.2;  
 
LO 4.A.2.1, SP 6.4 
 
 
3 points 
 
Derive an equation for the acceleration of the blocks after release in terms of 
A
m , 
B
m , and physical 
constants, as appropriate. If you need to draw anything other than what you have shown in part (b) to assist 
in your solution, use the space below. Do NOT add anything to the figure in part (b). 
 
For using separate Newton’s second law equations for each block  
 
1 point

For combining the equations with correct notation, including correctly using 
A
m  and

B
m , indicating that the same tension force acts on both blocks, and that they share 
the same acceleration

For a correct equation for a with supporting work: 
B

Alternate Solution: 
 
For writing a “whole-system” equation for the total mass that does not contain internal 
forces.

For substituting the net force and system mass with correct quantities  


B
A
B
m g
m
m
a


 
 
1 point

Note: Writing the correct whole-system equation is sufficient to earn the first two points.

(d)  
LO 3.A.1.1, SP 2.2; LO 3.A.3.1, SP 6.4; LO 3.B.1.3, SP 2.2 
 
 
1 point 
 
Consider the scenario from part (a)(ii), where the mass of block A is much less than the mass of block B. 
Does your equation for the acceleration of the blocks from part (c) agree with your reasoning in part 
(a)(ii)?

____ Yes          ____ No 
 
Briefly explain your reasoning by addressing why, according to your equation, the acceleration becomes 
(or approaches) a certain value when 
A
m  is much less than 
B
m .

Note: “No” is acceptable if the equation is inconsistent with the answer in (a)(ii).

For valid reasoning that addresses the result in part (c) and the reasoning in part (a)(ii) 
 
1 point

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Question 2 (continued) 
 
(d) (continued) 
 
Claims: 
Yes, the equation for the acceleration of the blocks from part (c) agrees with the 
reasoning in part (a)(ii). 
or 
No, the equation for the acceleration of the blocks from part (c) does not agree with 
the reasoning in part (a)(ii). 
 
Evidence: 
The mass of block A is much less than the mass of block B.

m
a
g
m
m


 (derived as part (c) answer)

Reasoning for “Yes” claim: 
When 
A
m  is much less than 
B
m , it can be neglected in the equation derived in  
part (c), giving an acceleration close to g as stated in (a)(ii). 
Reasoning for “No” claim, if the answer in part (a)(ii) is wrong: 
When 
A
m  is much less than 
B
m , it can be neglected in the equation derived in  
part (c), giving an acceleration close to g. This disagrees with the value of ___ stated 
in (a)(ii). 
Reasoning for “No” claim, if the answer in part (c) is wrong: 
When 
A
m  is much less than 
B
m , it can be neglected in the equation derived in  
part (c), giving an acceleration of ___. This disagrees with the value of g stated  
in (a)(ii).

(e) 
LO 3.A.1.1, SP 2.2; LO 3.B.1.1, SP 6.4,7.2; LO 3.B.1.3, SP 2.2 
 
 
2 points 
 
While the blocks are accelerating, the tension in the vertical portion of the string is 1T . Next, the pulley of 
negligible mass is replaced with a second pulley whose mass is not negligible. When the blocks are 
accelerating in this scenario, the tension in the vertical portion of the string is 2
T . How do the two 
tensions compare to each other?

____ 
2
1
T
T

          ____ 
2
1
T
T

          ____ 
2
1
T
T


Correct answer: 
2
1
T
T

.  
Note: A maximum of 1 point can be earned if an incorrect selection is made.

For reasoning that the acceleration of both blocks is smaller 
 
1 point

For doing any one of the following, consistent with the answer selection and Newton’s 
second law for block B 
 
Concluding that a smaller acceleration implies that 2
T  is greater than 1T  
 
Concluding that an unchanged acceleration implies that 2
T  is the same as 1T  
 
Concluding that a larger acceleration implies that 2
T  is less than 1T

Scene 10

Question 2 (continued) 
(e) (continued) 
 
Claim: 
2
1
T
T

 
Evidence: 
The pulleys spin with negligible friction about the axle. 
The original pulley has negligible mass. 
The second pulley’s mass is not negligible. 


F
a
m
 

Reasoning:  
The rotational inertia of the second pulley results in a smaller acceleration for the 
blocks. Block B must have a smaller net force to have a smaller acceleration, so the 
rope tension must be larger than before (closer in magnitude to the gravitational 
force on block B).

Learning Objectives 
 
LO 2.B.1.1: The student is able to apply F = mg 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. [See 
Science Practices 2.2, 7.2] 
LO 3.A.1.1: The student is able to express the motion of an object using narrative, mathematical, and graphical 
representations. [See Science Practices 1.5, 2.1, 2.2] 
LO 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. [See Science Practice 1.1] 
LO 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. 
[See Science Practices 6.4, 7.2] 
LO 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. [See Science Practices 6.4, 7.2] 
LO 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. [See Science 
Practices 1.5, 2.2] 
LO 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. [See Science Practices 1.1, 1.4, 2.2] 
LO 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. [See Science Practice 6.4]

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A projectile launcher consists of a spring with an attached plate, as shown in Figure 1. When the spring is 
compressed, the plate can be held in place by a pin at any of three positions A, B, or C. For example, Figure 2 
shows a steel sphere placed against the plate, which is held in place by a pin at position C. The sphere is 
launched upon release of the pin.

A student hypothesizes that the spring constant of the spring inside the launcher has the same value for 
different compression distances.

(a) i. and ii. 
 
LO 5.B.5.5, SP 2.2 
 
 
3 points 
 
The student plans to test the hypothesis by launching the sphere using the launcher.  
 
i. State a basic physics principle or law the student could use in designing an experiment to test the 
hypothesis. 
 ii. Using the principle or law stated in part (a)(i), determine an expression for the spring constant in 
terms of quantities that can be obtained from measurements made with equipment usually found in a 
school physics laboratory. 
 
For an equation that is consistent with a relevant principle or law as written in (a)(i) 
 
1 point

For a valid equation that contains measurable quantities and includes spring constant 
 
1 point

For a correct and valid algebraic expression for spring constant. The expression must be 
solved for k. 
 
1 point

(b)  
LO 3.A.1.2, SP 4.2; LO 4.C.1.1, SP 2.2; LO 5.B.3.3, SP 1.4, 2.2; LO 5.B.5.2, SP 4.2 
 
 
5 points 
 
 
Design an experimental procedure to test the hypothesis in which the student uses the launcher to launch 
the sphere. Assume equipment usually found in a school physics laboratory is available.

In the table below, list the quantities and associated symbols that would be measured in your experiment. 
Also list the equipment that would be used to measure each quantity. You do not need to fill in every row. 
If you need additional rows, you may add them to the space just below the table.

Quantity to be Measured 
Symbol for Quantity 
Equipment for Measurement

Scene 12

Describe the overall procedure to be used to test the hypothesis that the spring constant of the spring 
inside the launcher has the same value for different compression distances, referring to the table. Provide 
enough detail so that another student could replicate the experiment, including any steps necessary to 
reduce experimental uncertainty. As needed, use the symbols defined in the table and/or include a simple 
diagram of the setup.

For listing relevant/appropriate equipment that matches all measured quantities in the 
experimental procedure 
Note: This point can be earned if the sphere is not launched.

For describing measurements of quantities sufficient to determine the spring constant  
Note: This point can be earned if the sphere is not launched.

For a plausible procedure (i.e., can be done in a typical school physics lab) that involves 
launching the sphere to determine the spring constant  
 
1 point

For launching the sphere from at least 2 different initial positions 
 
1 point

For attempting to reduce uncertainty (e.g., multiple trials at a pin setting) 
Note: This point can be earned if the sphere is not launched.

Mass of sphere 
S
m   
Triple beam balance

Spring compression distance 
x

  
Ruler

Launch speed of sphere 
Lv   
Motion sensor

The mass of the sphere is measured with a triple beam balance. The launcher is aimed horizontally on a 
level surface toward a motion sensor. The spring is compressed to pin position A and the spring 
compression distance is measured. The mass is launched. The motion sensor measures launch speed. 
The process is repeated three times at position A. The procedure is repeated with the spring compressed 
to pin positions B and C.

Vertical displacement of sphere 
y
  
Meterstick

The launcher is aimed horizontally at a height above the ground so that the sphere will follow a 
projectile path and land on the floor. The spring is compressed to pin position A and the sphere is 
launched. Measure the mass of the sphere, the initial spring compression, and the vertical and horizontal 
displacements of the sphere from release to landing position. Repeat three times at pin position A. The 
procedure is repeated with the spring compressed to pin positions B and C.

Scene 13

Aim the launcher vertically. Compress the spring to pin position A. Launch the sphere vertically. 
Measure the mass of the sphere, the initial spring compression, and vertical displacement of the sphere 
above the release position. Repeat three times at pin position A. Repeat the procedure with the spring 
compressed to pin positions B and C.

(c)  
LO 3.A.1.3, SP 5.1; LO 4.C.1.1, SP 2.2; LO 5.A.2.1, SP 6.4; LO 5.B.3.3, SP 1.4, 2.2 
 
 
2 points 
 
Describe how the experimental data could be analyzed to confirm or disconfirm the hypothesis that the 
spring constant of the spring inside the launcher has the same value for different compression distances. 
 
For comparing the measurements of the spring constant (or a suitable proxy) at all three 
possible compression distances (A, B, C) 
 
1 point

For considering uncertainties in confirming the hypothesis (e.g., “If numbers match 
within experimental uncertainty,” or “If the numbers are about the same”)  
Note: This point is not earned for saying “if the numbers are the same” or similar

phrasing that does not address experimental uncertainty.

Example Analysis 1: 
For each pin position, take the average L-avg
v
  of the launch speeds measured at that position. Calculate

the spring constant k using the energy conservation relation 

2
2
L-avg
1
1
2
2
S
k
x
m v


 or


2
2
L-avg
S
k
m v
x


. Then compare the k values for each spring position. If the values agree within

experimental uncertainty, then the hypothesis is confirmed.

Example Analysis 2: 
For each pin position, take the averages 
avg
x

 and 
avg
y

 of the horizontal and vertical sphere

displacements. Calculate the time interval 
t

 using the kinematics equation 

2
avg
1
2
y
g
t



, and

then calculate the launch speed 
avg
L
v
x
t
 
 . Calculate the spring constant using the relation

2
2
L
S
k
m v
d

. Compare the k values for each spring position. If the values agree within 
experimental uncertainty, then the hypothesis is confirmed.

Scene 14

Example Analysis 3: 
For each pin position, take the average 
avg
y

 of the maximum vertical sphere displacement. Use

conservation of energy to calculate a value for the spring constant k from the equation

2
avg
1
2 kd
mg y


 (if measuring height from the release (pin) position)



2
avg
1
2 kd
mg
y
d



 (if measuring height from the spring’s uncompressed position)

Compare the k values for each spring position. If the values agree within experimental uncertainty, 
then the hypothesis is confirmed.

(d)  
LO 3.B.1.1, SP 6.4; LO 5.B.4.2, SP 1.4, 2.2 
 
 
2 points 
 
Another student uses the launcher to consecutively launch several spheres that have the same diameter but 
different masses, one after another. Each sphere is launched from position A. Consider each sphere’s launch 
speed, which is the speed of the sphere at the instant it loses contact with the plate. On the axes below, sketch 
a graph of launch speed as a function of sphere mass.

For a curve where launch speed always decreases with increasing sphere mass 
 
1 point

For a curve that is entirely concave up AND has the launch speed always decreasing 
with increasing sphere mass 
 
1 point

Scene 15

Learning Objectives 
 
LO 3.A.1.2: The student is able to design an experimental investigation of the motion of an object. [See Science 
Practice 4.2] 
LO 3.A.1.3: The student is able to analyze experimental data describing the motion of an object and is able to 
express the results of the analysis using narrative, mathematical, and graphical representations. [See Science 
Practice 5.1] 
LO 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. [See Science Practices 6.4, 7.2] 
LO 4.C.1.1: The student is able to calculate the total energy of a system and justify the mathematical routines 
used in the calculation of component types of energy within the system whose sum is the total energy. [See 
Science Practices 1.4, 2.1, 2.2] 
LO 5.A.2.1: The student is able to define open and closed systems for everyday situations and apply conservation 
concepts for energy, charge, and linear momentum to those situations. [See Science Practices 6.4, 7.2] 
LO 5.B.3.3: The student is able to apply mathematical reasoning to create a description of the internal potential 
energy of a system from a description or diagram of the objects and interactions in that system. [See Science 
Practices 1.4, 2.2] 
LO 5.B.4.2: The student is able to calculate changes in kinetic energy and potential energy of a system, using 
information from representations of that system. [See Science Practices 1.4, 2.1, 2.2] 
LO 5.B.5.2: The student is able to design an experiment and analyze graphical data in which interpretations of the 
area under a force-distance curve are needed to determine the work done on or by the object or system. [See 
Science Practices 4.2, 5.1] 
LO 5.B.5.5: The student is able to predict and calculate the energy transfer to (i.e., the work done on) an object or 
system from information about a force exerted on the object or system through a distance. [See Science 
Practices 2.2, 6.4]

Scene 16

A motor is a device that when connected to a battery converts electrical energy into mechanical energy. The 
motor shown above is used to lift a block of mass M at constant speed from the ground to a height H above 
the ground in a time interval t
 . The motor has constant resistance and is connected in series with a resistor 
of resistance 
1
R  and a battery.  
Mechanical power, the rate at which mechanical work is done on the block, increases if the potential 
difference (voltage drop) between the two terminals of the motor increases. 
 
(a)  
LO 5.B.5.5, SP 2.2 
 
 
2 points 
 
Determine an expression for the mechanical power in terms of M, H, t
 , and physical constants, as 
appropriate. 
 
For an expression that implies reasoning in terms of energy (as opposed to e.g., 
kinematics) 
 
1 point

For a correct expression for the power generated by the motor lifting the block at 
constant speed 
 
1 point

(b) 
LO 5.B.9.2, SP 4.2, 6.4, 7.2; LO 5.B.9.3, SP 6.4, 7.2 
 
 
5 points 
 
 
Without M or H being changed, the time interval t
  can be decreased by adding one resistor of  
resistance 
2
R , where 
2
1
R
R

, to the circuit shown above. How should the resistor of resistance 
2
R   
be added to the circuit to decrease t
  ?

___ In parallel with          ___ In parallel          ___ In parallel with          ___ In series with the battery,  
 
the battery 
with 
1
R  
the motor 
1
R , and the motor 
 
In a clear, coherent, paragraph-length response that may also contain figures and/or equations, justify why 
your selection would decrease t
 . 
 
Correct answer: “In parallel with 
1
R ”

Note: If the wrong selection is made, the justification may still earn credit.

Scene 17

Question 4 (continued) 
 
(b) (continued) 
 
For a justification that correctly asserts that power must increase for t
  to decrease, or 
correctly asserting that the faster the rate of energy transfer means that works gets done 
in a smaller time interval

For a correct assertion that current increases as resistance of the circuit decreases  
 
Alternate Method: Potential difference across the parallel resistors will decrease if their 
resistance decreases.

For making the connection that there is an increase in current specifically in the motor 
because it is the same as the total current in the circuit 
 
Alternate Method: There is an increase in potential difference specifically across the 
motor because the potential difference across the parallel resistors decreases 
(Kirchhoff’s loop rule).

For a justification that indicates that connecting 
2
R  in parallel with 
1
R  will decrease the 
equivalent resistance of the circuit 
 
1 point

For a logical, relevant, and internally consistent argument that addresses the required 
argument or question asked, and follows the guidelines described in the published 
requirements for the paragraph-length response

Example Paragraph Response 1: 
 
 
The work required to lift the block is MgH, so the rate at which the motor must do 
work to lift the block in the given time is W
t
MgH
t
 
 . The rate at which the 
motor does work increases with the potential difference across the motor (Note: 
This information is given in the question, so no points allotted in rubric for this 
statement.) To decrease the time, the motor must increase the rate at which the work 
is done, which requires a larger potential difference across the motor (or a larger 
current through the motor because 
V
IR


). To increase the potential difference 
across the motor, the potential difference across 
1
R  must decrease, by Kirchhoff’s 
loop rule (for a loop containing the battery, the motor and 
1
R ). When 
2
R  is placed 
in parallel with 
1
R  the equivalent resistance of the combination decreases and the 
potential difference across that section decreases.

Example Paragraph Response 2: 
 
 
Resistor 
2
R  should be connected in parallel with 
1
R . This will result in a smaller 
equivalent resistance in series with the battery and motor, so the current in the circuit 
(and through the motor) will be larger. The larger motor current results in the motor 
having a higher mechanical power. Because this power MgH
t
  is larger and MgH 
is constant, the time interval t
  will be smaller.

Scene 18

Learning Objectives 
 
LO 5.B.5.5: The student is able to predict and calculate the energy transfer to (i.e., the work done on) an object or 
system from information about a force exerted on the object or system through a distance. [See Science 
Practices 2.2, 6.4] 
LO 5.B.9.2: The student is able to apply conservation of energy concepts to the design of an experiment that will 
demonstrate the validity of Kirchhoff’s loop rule (ΣΔV = 0) in a circuit with only a battery and resistors either 
in series or in, at most, one pair of parallel branches. [See Science Practices 4.2, 6.4, 7.2] 
LO 5.B.9.3: The student is able to apply conservation of energy (Kirchhoff’s loop rule) in calculations involving 
the total electric potential difference for complete circuit loops with only a single battery and resistors in 
series and/or in, at most, one parallel branch. [See Science Practices 2.2, 6.4, 7.2]

Scene 19

A tuning fork vibrating at 512 Hz is held near one end of a tube of length L that is open at both ends, as 
shown above. The column of air in the tube resonates at its fundamental frequency. The speed of sound in air 
is 340 m s . 
 
(a)  
LO 6.D.3.4, SP 1.2; LO 6.D.4.2, SP 2.2 
 
 
2 points 
 
Calculate the length L of the tube.


 

340 m s
512 Hz
0.66 m
 


For a length that is half of the calculated wavelength, with units 
 
1 point

(b)  
LO 6.A.1.2, SP 1.2; LO 6.D.3.2, SP 6.4; LO 6.D.3.4, SP 1.2; LO 6.D.4.2, SP 2.2 
 
 
3 points 
 
The column of air in the tube is still resonating at its fundamental frequency. On the axes below, sketch a 
graph of the maximum speed of air molecules as they oscillate in the tube, as a function of position x, from  
x = 0 (left end of tube) to x = L (right end of tube). (Ignore random thermal motion of the air molecules.)

For a curve with a node (zero) at 
2
L
 
 
1 point

For a curve with maxima at 0, L, and no other points 
 
1 point

For a nonhorizontal curve that is symmetric around 
2
L
 and nonnegative everywhere 
 
1 point

Scene 20

(c)  
LO 6.D.3.4, SP 1.2; LO 6.D.4.2, SP 2.2) 
 
 
2 points 
 
The right end of the tube is now capped shut, and the tube is placed in a chamber that is filled with another 
gas in which the speed of sound is 1005 m s . Calculate the new fundamental frequency of the tube. 
 
Correct answer: 757 Hz

For an indication that the fundamental wavelength is 4L 
 
1 point

For substituting the new sound speed in v
f


  
 
1 point

Learning Objectives 
 
LO 6.A.1.2: The student is able to describe representations of transverse and longitudinal waves. [See Science 
Practice 1.2] 
LO 6.D.3.2: The student is able to predict properties of standing waves that result from the addition of incident 
and reflected waves that are confined to a region and have nodes and antinodes. [See Science Practice 6.4] 
LO 6.D.3.4: The student is able to describe representations and models of situations in which standing waves 
result from the addition of incident and reflected waves confined to a region. [See Science Practice 1.2] 
LO 6.D.4.2: The student is able to calculate wavelengths and frequencies (if given wave speed) of standing waves 
based on boundary conditions and length of region within which the wave is confined, and calculate 
numerical values of wavelengths and frequencies. Examples should include musical instruments. [See Science 
Practice 2.2]

AP Physics 1 Scoring Guidelines from the 2019 Exam Administration

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