AP Physics C: Mechanics Unit 7 practice questions

Question 1

A block of mass m oscillates vertically on a spring with constant k inside an elevator accelerating upward at a. Which claim about the period T is correct based on the spring-mass model?

Accepted Answer

T remains 2π√(m/k) because the uniform inertial force only shifts the equilibrium position.

Answer

T decreases because the effective gravity g+a increases the restoring force on the mass.

Answer

T increases because the effective gravity g-a decreases the restoring force on the mass.

Answer

T changes because the amplitude of oscillation is reduced by the upward acceleration force.

Question 2

A simple pendulum of length L hangs in a cart accelerating horizontally at a. Which claim about the new period T is justified by the pendulum model?

Accepted Answer

T decreases because the effective gravitational acceleration magnitude increases to √(g²+a²).

Answer

T increases because the effective gravitational acceleration magnitude increases to √(g²+a²).

Answer

T increases because the effective gravitational acceleration magnitude decreases to √(g²-a²).

Answer

T stays constant because the period depends only on the vertical component of acceleration.

Question 3

An ideal spring of constant k is cut into two equal lengths, and a mass m is suspended from one half. Which claim describes the new period T_new compared to the original period T_old?

Accepted Answer

T_new = T_old/√(2) because the spring constant doubles when the length is halved.

Answer

T_new = T_old/2 because the spring constant quadruples when the length is halved.

Answer

T_new = T_old√(2) because the spring constant halves when the length is halved.

Answer

T_new = 2T_old because the spring constant quarters when the length is halved.

Question 4

A particle of mass m moves such that its acceleration a is given by a = -Cx, where C is a positive constant. Which claim about the period T is justified by this relationship?

Accepted Answer

T = 2π/√(C) because the constant C represents the square of the angular frequency.

Answer

T = 2π√(C) because the constant C represents the inverse square of angular frequency.

Answer

T = 2π/C because the constant C represents the angular frequency of the motion directly.

Answer

T = 2πC because the constant C represents the inverse of the angular frequency directly.

Question 5

A block of mass $$m$$ attached to a spring with constant $$k$$ oscillates with amplitude $$A$$. How does the magnitude of the block's acceleration at position $$x = A$$ compare to its acceleration at position $$x = A/2$$?

Accepted Answer

It is two times greater at $$x = A$$

Answer

It is four times greater at $$x = A$$

Answer

It is the same at both positions

Answer

It is half as large at $$x = A$$

Question 6

Two identical springs are attached to blocks of mass $m$ and $4m$ . Both systems oscillate with the same amplitude $A$ . How does the maximum speed $v_1$ of the block with mass $m$ compare to the maximum speed $v_2$ of the block with mass $4m$ ?

$v_1$ is one-fourth of $v_2$

$v_1$ is one-half of $v_2$

$v_1$ is twice as large as $v_2$

$v_1$ is four times as large as $v_2$

Accepted Answer

$$v_1$$ is twice as large as $$v_2$$

Answer

$$v_1$$ is one-fourth of $$v_2$$

Answer

$$v_1$$ is one-half of $$v_2$$

Answer

$$v_1$$ is four times as large as $$v_2$$

Question 7

A spring with constant $$k$$ and mass $$m$$ oscillates horizontally. The same system is then hung vertically. How do the period $$T$$ and equilibrium position $$x_{eq}$$ of the vertical system compare to the horizontal system?

Accepted Answer

$$T$$ is the same; $$x_{eq}$$ is different

Answer

$$T$$ is greater; $$x_{eq}$$ is different

Answer

$$T$$ is smaller; $$x_{eq}$$ is the same

Answer

$$T$$ is the same; $$x_{eq}$$ is the same

Question 8

A particle undergoes simple harmonic motion. If the amplitude of oscillation is doubled from $$A$$ to $$2A$$, how does the new period $$T_{new}$$ compare to the original period $$T_{old}$$?

Accepted Answer

$$T_{new} = 1.0 T_{old}$$

Answer

$$T_{new} = 0.5 T_{old}$$

Answer

$$T_{new} = 1.4 T_{old}$$

Answer

$$T_{new} = 2.0 T_{old}$$

Question 9

A block oscillates on a horizontal spring. How does the magnitude of acceleration $$a_{eq}$$ at the equilibrium position compare to the magnitude of acceleration $$a_{turn}$$ at the turning points?

Accepted Answer

$$a_{eq}$$ is zero while $$a_{turn}$$ is maximum

Answer

$$a_{eq}$$ is maximum while $$a_{turn}$$ is zero

Answer

$$a_{eq}$$ and $$a_{turn}$$ are both zero

Answer

$$a_{eq}$$ and $$a_{turn}$$ are both maximum

Question 10

Two blocks with masses $$m$$ and $$3m$$ are attached to identical springs with constant $$k$$ and extended to the same amplitude $$A$$. How does the magnitude of acceleration $$a_1$$ of the lighter block compare to $$a_2$$ of the heavier block at the moment of release?

Accepted Answer

$$a_1$$ is three times the magnitude of $$a_2$$

Answer

$$a_1$$ is one-third the magnitude of $$a_2$$

Answer

$$a_1$$ is equal to the magnitude of $$a_2$$

Answer

$$a_1$$ is nine times the magnitude of $$a_2$$

AP Physics C: Mechanics Unit 7 Practice Test

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