Q: A uniform board of mass 20.0 kg is supported by the floor at one end and by a vertical rope at the other. A 50.0-kg person stands three-fourths of the length from the floor end. Which equation correctly represents the sum of all torques about the point where the board touches the floor, assuming the board makes an angle $$\alpha$$ with the horizontal and has length $$L$$?

$$T \cdot L \cdot \sin\alpha - m_{\text{board}} \cdot g \cdot \frac{L}{2} \cdot \sin\alpha - m_{\text{person}} \cdot g \cdot \frac{3L}{4} \cdot \sin\alpha = 0$$

Question 1

A uniform board of mass 20.0 kg is supported by the floor at one end and by a vertical rope at the other. A 50.0-kg person stands three-fourths of the length from the floor end. Which equation correctly represents the sum of all torques about the point where the board touches the floor, assuming the board makes an angle $$\alpha$$ with the horizontal and has length $$L$$?

Accepted Answer

$$T \cdot L \cdot \sin\alpha - m_{	ext{board}} \cdot g \cdot \frac{L}{2} \cdot \sin\alpha - m_{	ext{person}} \cdot g \cdot \frac{3L}{4} \cdot \sin\alpha = 0$$

Question 2

Which of the following is the first condition for equilibrium for an object at rest?

Accepted Answer

$$\sum \vec{F} = 0$$

Question 3

A glider of mass $$m is $$attached to an ideal spring with force constant $$k on a $$frictionless surface. What is the angular frequency $$\omega of $$its simple harmonic motion?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 4

A mass attached to a spring oscillates with amplitude $$A. $$What is the total distance it travels in one period?

Accepted Answer

$$2A$$

Question 5

Which of the following best describes the restoring force in simple harmonic motion for a spring-mass system?

Accepted Answer

$$F_x = -kx$$

Question 6

A mass is attached to a vertical spring and oscillates up and down in simple harmonic motion. If the mass is moving upward and has passed the equilibrium point, taking upward as positive $$x$$, which statement is correct?

Accepted Answer

Velocity is positive, acceleration is negative

Question 7

The displacement in simple harmonic motion as a function of time is given by $$x = A \cos(\omega t + \phi). $$What does $$\phi$$ represent?

Accepted Answer

Phase angle

Question 8

For a simple harmonic oscillator, which equation correctly relates the period $$T to $$the mass $$m$$ and spring constant $$k$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Question 9

A 2.45 N object is attached to a spring and oscillates with a period of 0.64 s. What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{4\pi^2$ m}{T^2$}$$

Question 10

Which moment corresponds to the maximum potential energy in a spring-mass system undergoing simple harmonic motion?

Accepted Answer

When the mass is at maximum displacement ($$x = \pm A)$$

Question 11

If the frequency of a simple harmonic oscillator is $$f$$, what is the angular frequency $$\omega$$?

Accepted Answer

$$\omega = 2\pi f$$

Question 12

A glider is displaced to the right from equilibrium on a frictionless surface attached to a spring. What is the direction of the restoring force and acceleration?

Accepted Answer

Both restoring force and acceleration are to the left

Question 13

Which of the following is the second condition for equilibrium for a nonrotating object?

Accepted Answer

$$\sum \vec{	au} = 0$$

Question 14

A pendulum clock uses a swinging pendulum to keep time. Which property of periodic motion is most directly responsible for the accuracy of the clock?

Accepted Answer

The period $$T of $$the pendulum

Question 15

If the displacement in SHM is $$x = A \cos(\omega t + \phi)$$, what is the velocity as a function of time?

Accepted Answer

$$v = -A \omega \sin(\omega t + \phi)$$

Question 16

A spring-mass system has amplitude $$A$$ and mass $$m. $$What is the total mechanical energy in the system?

Accepted Answer

$$E = \frac{1}{2} k A^2$

Question 17

Which of the following statements about the center of gravity is correct?

Accepted Answer

The center of gravity is the point where the weight of the object acts

Question 18

A spring-mass oscillator is displaced to $$x = -A. $$What are the signs of velocity and acceleration at this instant?

Accepted Answer

Velocity is zero, acceleration is positive

Question 19

If the period of a simple harmonic oscillator is $$T = 2\pi \sqrt{\frac{m}{k}}$$, what happens to the period if the mass is quadrupled?

Accepted Answer

The period doubles

Equilibrium and Simple Harmonic Motion: Study Notes for College Physics

Study Guide - Practice Questions

Study Guide - Flashcards