Question 1

A 0.5 kg mass is attached to a vertical ideal spring and oscillates with amplitude 0.2 m. If the spring constant is $$k = 10\ \mathrm{N/m}$$, what is the total mechanical energy of the system?

Accepted Answer

$$E = 0.4\ \mathrm{J}$$

Question 2

Which of the following correctly expresses Hooke's Law for a spring with equilibrium position $$y_0$$?

Accepted Answer

$$F_{\mathrm{spring}} = -k(y - y_0$)$$

Question 3

A mass $$m is $$suspended from a vertical spring and is at equilibrium. Which equation correctly relates the spring constant $$k$$, the equilibrium displacement $$y_0$$, and the mass $$m$$?

Accepted Answer

$$k y_0$ = m g$$

Question 4

The potential energy stored in a spring when it is stretched a distance $$y$$ from its equilibrium position is given by:

Accepted Answer

$$U = \frac{1}{2} k y^2$

Question 5

A 5 kg block is suspended from a spring and pulled 0.2 m below equilibrium, then released from rest. If its maximum speed is 1.0 m/s, what is the spring constant $$k$$?

Accepted Answer

$$k = 10\ \mathrm{N/m}$$

Question 6

Which of the following best describes the energy transformation in an ideal spring-mass system as it oscillates?

Accepted Answer

Kinetic energy and potential energy transform into each other, but their sum remains constant.

Question 7

If the displacement of a mass on a spring is given by $$y = A \cos \omega t$$, what is the expression for its velocity as a function of time?

Accepted Answer

$$v = -A \omega \sin \omega t$$

Question 8

For a mass-spring system, which of the following is the correct expression for the total mechanical energy in terms of amplitude $$A$$ and spring constant $$k$$?

Accepted Answer

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

Question 9

A student uses LoggerPro to measure the maximum velocity $$v_{\mathrm{max}}$$ and maximum displacement $$y_{\mathrm{max}} of a $$mass on a spring. Which equations should they use to calculate the kinetic and potential energy at these points?

Accepted Answer

$$K = \frac{1}{2} m v_{\mathrm{max}}^2$$, $$U = \frac{1}{2} k y_{\mathrm{max}}^2$$

Question 10

Which of the following statements about the equilibrium position of a mass-spring system is correct?

Accepted Answer

At equilibrium, the net force on the mass is zero.

Question 11

If a spring is stretched by 0.1 m and the spring constant is $$k = 50\ \mathrm{N/m}$$, what is the potential energy stored in the spring?

Accepted Answer

$$U = 0.25\ \mathrm{J}$$

Question 12

Which differential equation describes the motion of a mass $$m$$ attached to a spring with spring constant $$k$$?

Accepted Answer

$$m \frac{d^2$ y}{dt^2$} + k y = 0$$

Question 13

A mass on a spring oscillates with $$y = A \cos \omega t. At $$what position is the kinetic energy maximum?

Accepted Answer

At $$y = 0 ($$equilibrium position)

Question 14

Which of the following best describes the conservation of mechanical energy in an ideal spring system?

Accepted Answer

$$\Delta K + \Delta U = 0$$

Question 15

If the force probe in a spring experiment is not properly zeroed at the equilibrium position, what is the most likely effect on the calculated spring constant $$k$$?

Accepted Answer

The calculated $$k$$ will be inaccurate due to an offset in force measurements.

Question 16

A spring-mass system is oscillating. At which point is the potential energy of the spring zero?

Accepted Answer

At the equilibrium position ($$y = 0)$$

Question 17

In a vertical spring-mass system, what is the correct expression for the net force acting on the mass when displaced by $$y$$ from equilibrium?

Accepted Answer

$$F_{\mathrm{net}} = -k y$$

Question 18

A mass $$m$$ attached to a spring oscillates with angular frequency $$\omega. $$What is the relationship between $$\omega$$, $$k$$, and $$m$$?

Accepted Answer

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

Question 19

During a spring-mass experiment, a student finds $$v_{\mathrm{max}} = 0.5\ \mathrm{m/s}$$ and $$y_{\mathrm{max}} = 0.1\ \mathrm{m}$$ for a $$0.2\ \mathrm{kg}$$ mass and $$k = 8\ \mathrm{N/m}. $$What is the total mechanical energy?

Accepted Answer

$$E = 0.08\ \mathrm{J}$$

Potential and Kinetic Energy in Spring Systems: Physics I Study Notes

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