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AP Physics 1 · Unit 3 · Energy

Springs and Elastic Potential Energy Practice Problems

Connect spring deformation, restoring force, and elastic potential energy. Practice stretching, compression, spring launches, vertical equilibrium, and a spring bumper on a rough track.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Springs and Elastic Potential Energy lesson.Open interactive practice
A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Relate a spring’s force to its stored energy

Identify deformation and force direction

Measure extension or compression from natural length. Explain why a restoring force can oppose a cart’s current motion.

Calculate spring energy and work

Use spring stiffness and deformation to find stored energy. Compare equal stretching and compression and calculate work between two extensions.

Solve spring-launch situations

Combine elastic, gravitational, and kinetic energy in horizontal or vertical launches. Include resistance when a spring-driven cart enters a rough track.

A question from this set

A stretched spring and a moving cart

A cart attached to a horizontal spring is to the right of the spring’s relaxed position and is moving farther right. Ignore friction. In which direction does the spring exert a force on the cart?

  • Right, because that is the direction of motion.
  • Left, toward the relaxed position.
  • There is no spring force until the cart stops.
Try it in the practice set
A stretched spring and a moving cartA cart attached to a horizontal spring is to the right of the spring’s relaxed position and is moving farther right. Ignore friction. In which direction does the spring exert a force on the cart?CartVelocity →Relaxed positionSpring is stretched
The stretched spring’s cart is to the right of natural length and moving farther right.

Key ideas

Force and energy depend differently on deformation

The restoring force points toward natural length

Along the spring axis, Fspring = −kx when x is deformation from natural length. The minus sign describes the restoring direction.

Elastic potential energy depends on x²

Us = ½kx² is positive for either stretching or compression of an ideal spring. Doubling deformation multiplies stored energy by four.

See the physics

Compare deformation, force, and energy during release

Check your answer, then run the cart or switch stretching and compression trials. Watch the restoring force reverse as deformation changes, and compare stored energy with launch motion.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for springs and elastic potential energy?

Begin with a conceptual question, then work through the calculations.

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