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AP · AP 1 · free response

AP Physics 1: Algebra-Based · Question 10

AP Physics 1: Algebra-Based · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
discriminating
Marks
11
Topics
3
Answer
Complete
A sphere and a block released from the same height on two sections of one inclinetwo sections of the same inclineboth released from rest at the same heighthMMsphere rolls without slippingblock on a frictionless section
Fig. 10.1Two identical wedge-shaped inclines stand side by side on the same horizontal floor, labelled as two sections of the same incline. A solid sphere of mass M rests on the sloping face of the left wedge, and a block of mass M rests at the same point up the sloping face of the right wedge. A dashed horizontal line runs across the figure at the level of both objects, and a dimension line at the far left marks their common release height h above the floor. A note states that both are released from rest at the same height; a label under the left ramp reads that the sphere rolls without slipping, and one under the right ramp that the block is on a frictionless section.
free response11 marks

A solid sphere and a block have the same mass. Both are released from rest at the same height at the top of an incline. The sphere rolls down without slipping. The block slides down a frictionless section of the same incline. The moment of inertia of a solid sphere about its center is (2/5)MR².

  1. (a)

    Indicate Indicate which object reaches the bottom of the incline with the greater translational speed, or whether they arrive with the same speed. No justification is required in this part.

    1 mark
  2. (b)

    Derive Derive expressions for the translational speed of each object at the bottom of the incline, in terms of g and the height h.

    4 marks
  3. (c)

    Justify Use your expressions to justify the answer you gave in part (a).

    2 marks
  4. (d)

    Explain Explain, without using equations, why the sphere arrives more slowly, and explain why the answer does not depend on the mass or the radius of the sphere.

    4 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: 1 point: the block 1 point: block — Mgh = ½Mv², so v = √(2gh) 1 point: sphere — energy is shared between translation and rotation, Mgh = ½Mv² + ½Iω²
01

(a)

1 mark

Indicate Indicate which object reaches the bottom of the incline with the greater translational speed, or whether they arrive with the same speed. No justification is required in this part.

How to approach it

Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.

  1. 1

    1 point: the block

02

(b)

4 marks

Derive Derive expressions for the translational speed of each object at the bottom of the incline, in terms of g and the height h.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    1 point: block — Mgh = ½Mv², so v = √(2gh)

  2. 2

    1 point: sphere — energy is shared between translation and rotation, Mgh = ½Mv² + ½Iω²

  3. 3

    1 point: applies the rolling condition ω = v/R and substitutes I = (2/5)MR², giving Mgh = (7/10)Mv²

  4. 4

    1 point: v = √(10gh/7)

03

(c)

2 marks

Justify Use your expressions to justify the answer you gave in part (a).

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    1 point: compares the coefficients — 10/7 = 1.43 is smaller than 2, so the sphere's speed is smaller

  2. 2

    1 point: states the ratio explicitly, v_sphere / v_block = √(5/7) = 0.85

04

(d)

4 marks

Explain Explain, without using equations, why the sphere arrives more slowly, and explain why the answer does not depend on the mass or the radius of the sphere.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    1 point: both objects convert the same gravitational potential energy per unit mass

  2. 2

    1 point: the sphere must also spin as it moves, so part of that energy goes into rotational kinetic energy and less is left for translation

  3. 3

    1 point: the mass appears in every energy term and cancels, so it cannot affect the result

  4. 4

    1 point: the radius cancels because the rolling condition ties ω to v through the same R that appears in the moment of inertia — only the shape factor 2/5 survives

Private on this device

Did your answer earn the marks?

Compare the reasoning point by point, then choose what happens next.