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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 2: Force & Translational DynamicsSystems & Center of Mass

Systems & Center of Mass (College Board AP® Physics 1: Algebra-Based): Exam Questions

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11 mark
Three spheres on a horizontal line at coordinates 1m, 2m, and 4m, weighing 1kg, 2kg, and 8kg, respectively; x-axis labelled from 0 to 5m.

Three objects are arranged along the x-axis, as shown in the figure.

Which of the following is most nearly the location of the center of mass of the objects?

  • 3.0 space straight m from the origin

  • 2.4 space straight m from the 1 kg object

  • 0.6 space straight m from the 2 kg object

  • 0.4 space straight m from the 8 kg object

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2
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A car is modeled as a single-object system. Which of the following assumptions must be true for this model to be valid?

  • The car's internal structure significantly influences the forces acting on it.

  • The car's mass is distributed unevenly.

  • The car's center of mass can be used to describe the motion of the entire system.

  • External forces, such as friction, must act on different parts of the car independently.

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3
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Which of the following best describes the center of mass of a system?

  • The point at which all the system's mass is concentrated for motion analysis.

  • The geometric center of the system.

  • The point at which the greatest mass is located.

  • The point at which external forces can be ignored.

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4
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A system contains three particles with masses m subscript 1 space equals space 0.2 space straight g, m subscript 2 space equals space 0.3 space straight g and m subscript 3 space equals space 0.5 space straight g. The particles are located at positions open parentheses 1.0 comma space 0 close parentheses space straight m, open parentheses 2.0 comma space 0 close parentheses space straight m and open parentheses 4.0 comma space 0 close parentheses space straight m respectively. Which of the follwing gives the correct position of the system's centre of mass, x with rightwards arrow on top subscript c m end subscript?

  • 0.25 m

  • 0.28 m

  • 0.32 m

  • 0.38 m

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5
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Which row of the table correctly describes open and closed systems?

Open system

Closed system

A

Net external forces act

Mass is transferred

B

Total mechanical energy is not conserved

No external forces act

C

Total momentum is not conserved

Energy is transferred

D

Transfer of energy or mass

Total momentum is not conserved

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    1
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    Diagram showing a ramp with an object labelled M at the top, sliding down towards a block labelled 2M on a flat surface. Distance D is marked.

    A small block of mass M is released from the top of a curved frictionless ramp, as shown in the figure. The block slides down the ramp until it collides with a larger block of mass 2 M which is at rest at the bottom of the ramp. After the collision, the larger block moves along a rough horizontal surface before coming to rest after a distance D.

    By considering the mechanical energy of the two-block-Earth system, which of the following statements is correct, and why?

    • The system is open, because there is a net force exerted on the larger block.

    • The system is open, because the small block’s initial velocity and the larger block's final velocity is zero.

    • The system is closed, because there is a net force exerted on the larger block.

    • The system is closed, because the small block’s initial velocity and the larger block's final velocity is zero.

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    2
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    Grid with four horizontal and vertical lines. Points labelled 1-4, with weights annotated: 3 kg at top, 1 kg and 3 kg right, 7 kg bottom left.

    Four objects are arranged in a plane, as shown in the figure.

    Which of the following points represents the location of the center of mass of the objects?

    • 1

    • 2

    • 3

    • 4

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    3
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    Diagram of a ruler with numbers 1-17 balanced on a triangular pivot. A ring on 2, and two rings on 14. A labelled peg at the right end.

    A uniform rod is balanced on a pivot, as shown in the figure. Rings of equal mass are hung on different pegs, two on peg 14, and one on peg 2.

    If a fourth ring is hung on peg 6 to balance the rod, which of the following correctly describes how the center of mass of the system changes?

    • The center of mass shifts to the left by 1 peg

    • The center of mass shifts to the right by 1 peg

    • The center of mass shifts to the left by 2 pegs

    • The center of mass shifts to the right by 2 pegs

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    4
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    A block slides on a rough surface. As it travels, its speed decreases. The system is defined as the block and the surface. Which of the following is the correct classification of the system?

    • An isolated system, because the forces are internal.

    • A closed system, because no mass is exchanged.

    • An open system, because friction dissipates energy to the surroundings.

    • A closed system, because momentum is conserved.

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    5
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    In a system containing two objects that collide and remain stuck together, which of the following must be true?

    • The total mechanical energy is conserved.

    • Momentum is conserved, as the collision forces are internal.

    • Momentum is not conserved due to external forces.

    • Kinetic energy is conserved.

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    1
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    Diagram of a pulley system with a single rope. Block X hangs lower than block Y, both suspended by the pulley from the ceiling.

    Objects X and Y are connected by a string of negligible mass and suspended vertically over a pulley of negligible mass, as shown in the figure. The objects are initially held at rest, and the mass of Object Y is greater than the mass of Object X. All frictional forces are considered to be negligible.

    How do the mechanical energies of the two-object–string system and the two-object–string-Earth system change from when the objects are released to when they return to rest?

    Two-Object-String System

    Two-Object-String-Earth System

    A

    Decreases

    Increases

    B

    Increases

    Decreases

    C

    Decreases

    Remains Constant

    D

    Remains Constant

    Remains Constant

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      2
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      Two blocks,m subscript 1​ and m subscript 2, are connected by a light string and rest on a horizontal frictionless table. A force F is applied to m subscript 1​⁣ such that it pulls both blocks across the table. Assuming the system consists of both blocks and the string, which of the following is true about the net force and acceleration of the system?

      Net force

      Acceleration

      A

      F with rightwards arrow on top

      fraction numerator F with rightwards arrow on top over denominator m subscript 1 space plus space m subscript 2 end fraction

      B

      F with rightwards arrow on top

      fraction numerator F with rightwards arrow on top over denominator m subscript 1 space end fraction

      C

      fraction numerator F with rightwards arrow on top over denominator m subscript 2 end fraction

      fraction numerator F with rightwards arrow on top over denominator m subscript 1 space plus space m subscript 2 end fraction

      D

      F with rightwards arrow on top space minus space m subscript 1 g

      fraction numerator F with rightwards arrow on top over denominator m subscript 1 end fraction

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        3
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        A spacecraft travels through deep space, beyond the gravitational effects of any planetary bodies. The spacecraft accelerates by ejecting exhaust gases. If the system is defined as the spacecraft and its exhaust gases, which of the following correctly explains the momentum of the system?

        • The system's momentum decreases as mass is lost.

        • The system's momentum increases because the spacecraft speeds up.

        • The system's momentum remains constant because no external forces act.

        • The system's momentum cannot be determined without knowing the exhaust velocity.

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        4
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        Four objects lie within a two-dimensional system. The objects are located at the following positions: open parentheses 0.25 comma space 1.30 close parentheses space straight m, open parentheses 4.52 comma space 1.04 close parentheses space straight m, open parentheses 6.17 comma space 2.45 close parentheses space straight m and open parentheses 8.09 comma space 0.96 close parentheses space straight m. The masses of the objects are 5.29 space kg, 62.87 space kg, 0.57 space kg and 22.67 space kg respectively. Which of the following correctly describes the position vector of the system's centre of mass?

        • r with rightwards arrow on top subscript c m end subscript space equals space 4.52 space straight m at theta space equals space 42 degree

        • r with rightwards arrow on top subscript c m end subscript space equals space 4.87 space straight m at theta space equals space 29 degree

        • r with rightwards arrow on top subscript c m end subscript space equals space 5.01 space straight m at theta space equals space 89 degree

        • r with rightwards arrow on top subscript c m end subscript space equals space 5.27 space straight m at theta space equals space 11 degree

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        5
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        A triangular plate has uniform mass density and is located in the x-y plane with vertices at open parentheses 0 comma space 0 close parentheses, open parentheses 4 comma space 0 close parenthesesand open parentheses 0 comma space 3 close parentheses. Which of the following gives the correct position of the center of mass?

        • open parentheses 4 over 3 comma space 1 close parentheses

        • open parentheses 1 1 half comma space 2 close parentheses

        • open parentheses 1 3 over 4 comma space 2 close parentheses

        • open parentheses 2 comma space 3 over 4 close parentheses

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