AP Physics 1 Sample Student Responses and Scoring Commentary from the 2018 Exam Administration: Free Response Question 1

2018

AP Physics 1:

Algebra-Based

Sample Student Responses

and Scoring Commentary

Inside:

Free Response Question 1

• Scoring Guideline

• Student Samples

• Scoring Commentary

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PHYSICS

2018 SCORING GUIDELINES

General Notes About 2018 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 f

ound 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

subs

tituted 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

par

ticular 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.

The scoring guidelines typically show numerical results using the value

g = 9.8 m s

, but the use of

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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PHYSICS 1

2018 SCORING GUIDELINES

Question 1

7 points total Distribution

of points

A spacecraft of mass m is in a clockwise circular orbit of radius R around Earth, as shown in the figure above.

The mass of Earth is

(a) LO / SP: 3.A.2.1 / 1.1; 3.B.2.1 / 1.1, 1.4

2 points

In the figure below, draw and label the forces (not components) that act on the spacecraft. Each force must be

represented by a distinct arrow

starting on, and pointing away

from, the spacecraft.

For an arrow directed toward Earth’s center 1 point

For a correct label on the arrow representing the gravitational force, where the arrow is

pointi

ng toward Earth’s center

1 point

Note: A maximum of 1 point may be earned if extraneous forces are present.

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PHYSICS 1

2018 SCORING GUIDELINES

Question 1 (continued)

Distribution

of points

(b) LO / SP: 2.B.2.1 / 2.2; 3.A.1.1 / 1.5, 2.2; 3.B.1.3 / 1.5, 2.2; 3.B.2.1 / 1.1, 1.4, 2.2, 3.C.1.2 / 2.2

4 points

i. 3 points

Derive an equation for the orbital period T of the spacecraft in terms of m,

R, and physical constants,

as appropriate. If you need to draw anything other than what you have shown in part (a) to assist in your

solution, use the space below. Do NOT add anything to the figure in part (a).

For using (or implying) Newton’s second law and equating the centripetal force to the

gravitational force:

GmM

= ma=

1 point

For explicitly or implicitly determining that the speed of the spacecraft is:



v =

1 point

For a correct answer algebraically equivalent to:



T =

1 point

Note: It is acceptable to leave answer in ter

ms of



T =

ii. 1 point

A second spacecraft of mass 2m is placed in a circular orbit with the same radius R. Is the orbital period of

the second spacecraft greater than, less than, or equal to the orbi

tal period of the first spacecraft?

____ Greater than ____ Less than ____ Equal to

Briefly explain your reasoning.

Correct answer: “Equal to”

Note: For an incorrect answer consistent with part (b)(i), the

explanation is still graded

for consistency with part (b)(i).

For a correct explanation that the period of the spacecraft does not depend on the

spacecraft m

ass (or only depends on the mass of Earth and the radius of the orbit)

OR an explanation consistent with the answer from (b)(i)

1 point

Note: The explanation must be consistent with the checked answer.

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PHYSICS 1

2018 SCORING GUIDELINES

Question 1 (continued)

Distribution

of points

1 point

he first spacecraft is moved into a new circular orbit that has a radius greater than R, as shown in the

figure below.

Is the speed of the spacecraft in the new orbit greater than, less than, or equal to the original speed?

____ Greater than ____ Less than ____ Equal to

Briefly explain your reasoning.

Correct answer: “Less than”

Note: If the wrong selection is m

ade, the explanation is not graded.

For a correct explanation of why speed decreases with increasing orbital radius 1 point

Example:

Derivation step in (b)(i) shows that speed decreases with increasing R.

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PHYSICS 1

2018 SCORING GUIDELINES

Question 1 (continued)

Learning Objectives (LO)

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 and 7.2]

LO 2.B.2.1: The student is able to apply g = GM r

to calculate the gravitational field due to an object with

mass M, where the field is a vector directed toward the center of the object of mass M. [See Science

Practice 2.2]

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, and 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.B.1.3: The student is able to re-express 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 and 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, and 2.2]

LO 3.C.1.2: The student is able to use Newton's law of gravitation to calculate the gravitational force between

two objects and use that force in contexts involving orbital motion (for circular orbital motion only in

Physics 1). [See Science Practice 2.2]

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P1 Q1 A p1

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P1 Q1 A

P1 Q1 A p2

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P1 Q1 B p1

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P1 Q1 B

P1 Q1 B p2

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P1 Q1 C p1

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P1 Q1 C

P1 Q1 C p2

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PHYSICS 1

2018 SCORING COMMENTARY

Question 1

Overview

This question assessed learning objectives 2.B.1.1, 2.B.2.1, 3.A.1.1, 3.A.2.1, 3.B.1.3, 3.B.2.1, and 3.C.1.2.

The responses to this question were expected to demonstrate the following:

• The ability to construct free-body diagrams, only including the relevant forces without extraneous

forces.

• Recognition of cases in which the net force is centripetal in the context of universal gravitation.

• An understanding of how changing one quantity in an equation may or may not affect other quantities.

• Recognition that direct and inverse relationships only hold when other variables are kept constant.

Sample: Q1 P1 A

Score: 7

Part (a) earned 2 points. The response e

arned 1 point for an arrow directed toward Earth’s center, and the

response earned 1 point because the arrow is correctly and appropriately labeled as a gravitational force.

Part (b)(i) earned 3 points. The response earned 1 point because it uses Newton’s second law by equating the

centripetal force to the gravitational force exerted on the spacecraft. The response earned 1 point for determining

the speed of the spacecraft, which is substituted for v in the derivation. The response earned 1 point for a correct

algebraic answer. Part (b)(ii) earned 1 point for a correct explanation that the period of the spacecraft does not

depend on the spacecraft’s mass. Part (c) earned 1 point for a correct explanation of why the speed of the

spacecraft decreases with increasing orbital radius.

Sample: Q1 P1 B

Score: 5

Part (a) earned 2 points. The response e

arned 1 point for an arrow directed toward Earth’s center, and the

response earned 1 point because the arrow is correctly and appropriately labeled as a gravitational force.

Part (b)(i) earned 1 point because it uses Newton’s second law by equating the centripetal force to the

gravitational force exerted on the spacecraft. The response uses an incorrect expression for the speed, resulting

in an incorrect solution for the orbital period. Part (b)(ii) earned 1 point because the response is consistent with

the incorrect solution in part (b)(i); the response references that the (incorrect) derived equation for the

spacecraft’s period in part (b)(i) does not include the mass of the spacecraft. Part (c) earned 1 point for a correct

explanation of why the speed of the spacecraft decreases with increasing orbital radius.

Sample: Q1 P1 C

Score: 2

Part (a) earned 2 points. The response e

arned 1 point for an arrow directed toward Earth’s center, and the

response earned 1 point because the arrow is correctly and appropriately labeled as a gravitational force.

Part (b)(i) earned no points. The response does not use Newton’s second law or (in the designated answer space)

equate the centripetal force to the gravitational force exerted on the spacecraft. The response does not determine

the speed of the spacecraft or include a correct final answer. Part (b)(ii) earned no points. The incorrect response

is not consistent with the equations indicated in part (b)(i). Part (c) earned no points because the wrong selection

is indicated.

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