AP Physics C: Mechanics Practice Quiz: Spring Forces

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 10 questions to check your progress.

Question 1 of 10

Which of the following equations correctly represents Hooke's law for the force exerted by an ideal spring?

A)F = maB)k = FΔxC)Fₛ = kΔxD)Fₛ = -kΔx

All Questions (10)

Which of the following equations correctly represents Hooke's law for the force exerted by an ideal spring?

A) F = ma

B) k = FΔx

C) Fₛ = kΔx

D) Fₛ = -kΔx

Correct Answer: D

Hooke's law is given by the equation Fₛ = -kΔx, where the negative sign indicates that the spring force is a restoring force, acting in the direction opposite to the displacement.

In the equation for Hooke's Law, Fₛ = -kΔx, what does the negative sign signify?

A) The spring constant k is always a negative value.

B) The force exerted by the spring is always in the negative direction.

C) The force exerted by the spring is a restoring force, acting opposite to the direction of displacement.

D) The displacement Δx must be negative for the law to apply.

Correct Answer: C

The negative sign in Hooke's law indicates that the force exerted by the spring is a restoring force. This means it always acts in a direction opposite to the displacement of the object from its equilibrium position.

An ideal spring with a spring constant of 200 N/m is compressed by 0.1 m. What is the magnitude of the force exerted by the spring on the object causing the compression?

A) 2 N

B) 20 N

C) 200 N

D) 2000 N

Correct Answer: B

Using the magnitude of Hooke's Law, Fₛ = kΔx. Substituting the given values: Fₛ = (200 N/m) * (0.1 m) = 20 N.

Two ideal springs with spring constants k₁ = 50 N/m and k₂ = 100 N/m are connected in parallel. What is the equivalent spring constant of this combination?

A) 33.3 N/m

B) 75 N/m

C) 150 N/m

D) 5000 N/m

Correct Answer: C

For springs arranged in parallel, the equivalent spring constant is the sum of the individual spring constants. Therefore, k_eq = k₁ + k₂ = 50 N/m + 100 N/m = 150 N/m.

Two ideal springs with spring constants k₁ = 50 N/m and k₂ = 100 N/m are connected in series. What is the equivalent spring constant of this combination?

A) 33.3 N/m

B) 75 N/m

C) 150 N/m

D) 0.03 N/m

Correct Answer: A

For springs in series, the inverse of the equivalent spring constant is the sum of the inverses of the individual constants. 1/k_eq = 1/k₁ + 1/k₂ = 1/50 + 1/100 = 2/100 + 1/100 = 3/100. Therefore, k_eq = 100/3 ≈ 33.3 N/m.

According to Hooke's Law, if the displacement of an object from a spring's equilibrium is doubled, how does the magnitude of the spring's restoring force change?

A) It is halved.

B) It remains the same.

C) It is doubled.

D) It is quadrupled.

Correct Answer: C

The magnitude of the spring force is directly proportional to the displacement (Fₛ = kΔx). Therefore, if the displacement (Δx) is doubled, the magnitude of the force (Fₛ) will also be doubled.

Three identical ideal springs, each with a spring constant k, are arranged in parallel. What is the equivalent spring constant of the system?

A) k/3

B) k

C) 3k

D) k³

Correct Answer: C

For springs in parallel, the equivalent spring constant is the sum of the individual spring constants. With three identical springs, k_eq = k + k + k = 3k.

Three identical ideal springs, each with a spring constant k, are arranged in series. What is the equivalent spring constant of the system?

A) k/3

B) k

C) 3k

D) k/9

Correct Answer: A

For springs in series, the inverse of the equivalent spring constant is the sum of the inverses. So, 1/k_eq = 1/k + 1/k + 1/k = 3/k. Therefore, k_eq = k/3.

Which arrangement of two non-identical springs will result in a larger equivalent spring constant?

A) A parallel arrangement.

B) A series arrangement.

C) The arrangement does not affect the equivalent spring constant.

D) It depends on whether the springs are being stretched or compressed.

Correct Answer: A

In a parallel arrangement, k_eq = k₁ + k₂. In a series arrangement, k_eq is always less than the smallest individual spring constant. Therefore, the parallel arrangement always results in a larger (stiffer) equivalent spring constant.

Two ideal springs are connected in series. The first spring has a constant k₁, and the second has a constant k₂ = 2k₁. What is the equivalent spring constant of the combination in terms of k₁?

A) 3k₁

B) k₁/3

C) 3k₁/2

D) 2k₁/3

Correct Answer: D

Using the formula for springs in series: 1/k_eq = 1/k₁ + 1/k₂. Substitute k₂ = 2k₁: 1/k_eq = 1/k₁ + 1/(2k₁). Find a common denominator: 1/k_eq = 2/(2k₁) + 1/(2k₁) = 3/(2k₁). Inverting both sides gives k_eq = 2k₁/3.