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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedExam QuestionsUnit 2: Force & Translational DynamicsSpring Forces

Spring Forces (College Board AP® Physics 1: Algebra-Based): Exam Questions

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1
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Which of the following statements correctly describes the force exerted by an ideal spring on an object?

  • The force exerted by the spring on an object is always directed away from the equilibrium position.

  • The force exerted by the spring on an object is proportional to the mass of the object attached to it.

  • The force exerted by the spring on an object is proportional to the change in the spring’s length from its relaxed length.

  • The force exerted by the spring on an object decreases as the spring is stretched or compressed further from its relaxed length.

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2
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A spring with a spring constant of 150 space straight N divided by straight m is compressed by 10 space cm. What is the magnitude of the restoring force exerted by the spring?

  • 0.15 space straight N

  • 15.0 space straight N

  • 150.0 space straight N

  • 1500.0 space straight N

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3
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Two springs, each with a spring constant of 200 space straight N divided by straight m, are connected in series. What is the effective spring constant of the system?

  • 100 space straight N divided by straight m

  • 150 space straight N divided by straight m

  • 200 space straight N divided by straight m

  • 400 space straight N divided by straight m

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4
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A graph shows the force versus extension for a spring. Which statement about the graph is true?

  • The slope of the graph represents the spring constant

  • The area under the graph represents the spring constant

  • The slope of the graph represents the elastic potential energy

  • The area under the graph represents the displacement

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5
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If two identical springs are connected in parallel, how does the effective spring constant compare to the individual spring constants?

  • It is equal to the individual spring constant

  • It is half the individual spring constant

  • It is twice the individual spring constant

  • It is four times the individual spring constant

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1
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Two ideal springs with spring constants k subscript 1and k subscript 2are connected in series. A force F is applied to stretch the system. Which of the following gives the magnitude of the total extension of the system?

  • fraction numerator F over denominator k subscript 1 plus k subscript 2 end fraction

  • F over k subscript 1 space plus space F over k subscript 2

  • fraction numerator k subscript 1 plus k subscript 2 over denominator F end fraction

  • fraction numerator F open parentheses k subscript 1 plus k subscript 2 close parentheses over denominator k subscript 1 k subscript 2 end fraction

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2
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Which of the following combinations of springs will the effective spring constant be equal to k?

  • Diagram of a system with two springs and one block. Each spring, labeled as having a spring constant of 2k, is connected in series between a fixed end and the block.
  • Diagram of a system with four springs and one block. Each spring, labeled as having a spring constant of 1/4 k, is connected in series between a fixed end and the block.
  • Diagram of a system with two springs and one block. The springs, each labeled as having a spring constant of k, are connected in parallel between a fixed end and the block.
  • Diagram of a system with two springs and one block. The springs, each labeled as having a spring constant of 2k, are connected in parallel between a fixed end and the block.

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3
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A spring has a spring constant k of 200 space straight N divided by straight m and a relaxed length of 14 space cm. Which of the following gives the length of the spring when a force of 10 space straight N is used to compress the spring?

  • 5 space cm

  • 9 space cm

  • 13.95 space cm

  • 19 space cm

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4
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Three identical springs with spring constant k are arranged: two are connected in parallel, and one is in series with this parallel combination. If a force F is applied to stretch the system, what is the total extension of the system?

  • fraction numerator F over denominator 3 k end fraction

  • F over k

  • fraction numerator 3 F over denominator 2 k end fraction

  • fraction numerator 3 F over denominator k end fraction

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1
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The graph shown represents the results obtained when a spring was stretched with an increasing load. Which of the following gives the spring constant?

  • 0.080 space straight N divided by straight m

  • 0.13 space straight N divided by straight m

  • 2.7 space straight N divided by straight m

  • 8.0 space straight N divided by straight m

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2
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Two springs with spring constants k subscript 1 space equals space 200 space straight N divided by straight m and k subscript 2 space equals space 400 space straight N divided by straight m are connected in parallel. A 5.0 space kg mass is attached to the system and allowed to come to rest. The system is then pulled downward until the total extension reaches 10.0 space cm before being released.

Which of the following most nearly gives the maximum linear velocity of the system?

  • 0.89 space straight m divided by straight s

  • 1.1 space straight m divided by straight s

  • 1.58 space straight m divided by straight s

  • 2.68 space straight m divided by straight s

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3
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A hanging mass of 4.0 space kg is attached to a uniform spring with k space equals space 500 space straight N divided by straight m. A further mass 1 over 8 the value of the original mass is added to the spring to increase the extension.

Which of the following gives the ratio of the final potential energy in the spring-mass system in comparison to the initial potential energy in the spring-mass system?

  • 1.3

  • 1.6

  • 2.8

  • 4.5

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4
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A 3.0 space kg block is suspended from a vertical spring with a spring constant of 450 space straight N divided by straight m inside an elevator accelerating upwards at 2.0 space straight m divided by straight s squared. The block is then pulled downward 5.0 space cm from its new equilibrium position and released from rest.

Which of the following most nearly gives the maximum acceleration of the block relative to the Earth during its oscillation?

  • 0.08 space straight m divided by straight s squared

  • 29.5 space straight m divided by straight s squared

  • 30.0 space straight m divided by straight s squared

  • 58.5 space straight m divided by straight s squared

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