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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Spring Forces

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1
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1 mark

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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1 mark

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

  • 0.15 N

  • 15.0 N

  • 150.0 N

  • 1500.0 N

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3
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1 mark

Two springs, each with a spring constant of 200 N/m, are connected in series. What is the effective spring constant of the system?

  • 100 N/m

  • 150 N/m

  • 200 N/m

  • 400 N/m

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4
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1 mark

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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1 mark

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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1 mark

Two ideal springs with spring constants k1and k2are 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?

  • Fk1+k2

  • Fk1 + Fk2

  • k1+k2F

  • F(k1+k2)k1k2

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2
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1 mark

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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1 mark

A spring has a spring constant k of 200 N/m and a relaxed length of 14 cm. Which of the following is most nearly the length of the spring when an applied force of magnitude 10 N compresses the spring?

  • 5 cm

  • 9 cm

  • 14 cm

  • 19 cm

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4
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1 mark

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, which of the following expressions represents the total extension of the system?

  • F3k

  • Fk

  • 3F2k

  • 3Fk

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5
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1 mark
Line graph showing a linear increase, depicting length in cm versus load in N, with axes ranging from 0-15 cm and 0-0.5 N, respectively.

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 N/m

  • 0.13 N/m

  • 2.7 N/m

  • 8.0 N/m

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1
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1 mark

Two springs with spring constants k1 = 200 N/m and k2 = 400 N/m are connected in parallel. A 5.0 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 cm before being released.

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

  • 0.1 m/s

  • 0.2 m/s

  • 0.9 m/s

  • 1.1 m/s

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2
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1 mark

A hanging mass of 4.0 kg is attached to a uniform spring with k = 500 N/m. A further mass 18 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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3
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1 mark

A 3.0 kg block is suspended from a vertical spring with a spring constant of 450 N/m inside an elevator accelerating upwards at 2.0 m/s2. The block is then pulled downward 5.0 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 m/s2

  • 9.5 m/s2

  • 30.0 m/s2

  • 58.5 m/s2

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