Q: A spring with spring constant $$k = 2500\ \mathrm{N/m} is $$stretched by $$x = 0.10\ \mathrm{m}$$ and then released from rest. What is the maximum speed of a $$2\ \mathrm{kg}$$ mass attached to the spring as it passes through the equilibrium position ($$x = 0$$)?

$$v = \sqrt{\frac{k}{m}} x = \sqrt{\frac{2500}{2}} \times 0.10 = 3.54\ \mathrm{m/s}$$

Q: A $$10\ \mathrm{kg}$$ block compresses a spring ($$k = 3000\ \mathrm{N/m}) by$$ $$0.20\ \mathrm{m}$$ and is then released. What is the speed of the block as it leaves the spring (assuming a frictionless surface)?

$$v = \sqrt{\frac{kx^2$}{m}} = \sqrt{\frac{3000 \times (0.20)^2$}{10}} = 1.55\ \mathrm{m/s}$$

Q: A $$10\ \mathrm{kg}$$ block is released from rest after compressing a spring ($$k = 3000\ \mathrm{N/m}) by$$ $$0.20\ \mathrm{m}. $$How high will it rise up a frictionless incline before stopping?

$$h = \frac{\frac{1}{2}kx^2$}{mg} = \frac{\frac{1}{2} \times 3000 \times (0.20)^2$}{10 \times 9.8} = 0.61\ \mathrm{m}$$

Question 1

A spring with spring constant $$k = 2500\ \mathrm{N/m} is $$stretched by $$x = 0.10\ \mathrm{m}$$ and then released from rest. What is the maximum speed of a $$2\ \mathrm{kg}$$ mass attached to the spring as it passes through the equilibrium position ($$x = 0$$)?

Accepted Answer

$$v = \sqrt{\frac{k}{m}} x = \sqrt{\frac{2500}{2}} 	imes 0.10 = 3.54\ \mathrm{m/s}$$

Question 2

Which of the following best describes the physical meaning of the negative sign in Hooke’s Law $$F = -kx$$?

Accepted Answer

It indicates that the spring force always acts in the direction opposite to the displacement from equilibrium.

Question 3

A $$10\ \mathrm{kg}$$ block compresses a spring ($$k = 3000\ \mathrm{N/m}) by$$ $$0.20\ \mathrm{m}$$ and is then released. What is the speed of the block as it leaves the spring (assuming a frictionless surface)?

Accepted Answer

$$v = \sqrt{\frac{kx^2$}{m}} = \sqrt{\frac{3000 	imes (0.20)^2$}{10}} = 1.55\ \mathrm{m/s}$$

Question 4

Which equation gives the angular frequency $$\omega$$ for a mass-spring system?

Accepted Answer

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

Question 5

A marble is placed in a bowl and displaced from its equilibrium position. Which type of force acts to restore it to equilibrium?

Accepted Answer

A spring-like (restorative) force proportional to displacement

Question 6

If a spring is compressed by $$x$$ and then released on a frictionless table, what type of motion will the attached mass undergo?

Accepted Answer

Simple harmonic motion

Question 7

Which of the following is the correct expression for the potential energy stored in a spring compressed or stretched by $$x$$?

Accepted Answer

$$U = \frac{1}{2}kx^2$

Question 8

A $$2\ \mathrm{kg}$$ mass attached to a spring ($$k = 2500\ \mathrm{N/m}) is $$stretched $$0.10\ \mathrm{m}$$ and released. What is the period $$T of $$oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{2}{2500}} = 0.178\ \mathrm{s}$$

Question 9

Which statement about the conservation of energy in a mass-spring system is correct?

Accepted Answer

The total mechanical energy remains constant if there is no friction.

Question 10

A $$10\ \mathrm{kg}$$ block is released from rest after compressing a spring ($$k = 3000\ \mathrm{N/m}) by$$ $$0.20\ \mathrm{m}. $$How high will it rise up a frictionless incline before stopping?

Accepted Answer

$$h = \frac{\frac{1}{2}kx^2$}{mg} = \frac{\frac{1}{2} 	imes 3000 	imes (0.20)^2$}{10 	imes 9.8} = 0.61\ \mathrm{m}$$

Question 11

Which of the following materials has the highest Young’s modulus, indicating the greatest resistance to compression?

Accepted Answer

Steel

Question 12

What is the correct formula for the restoring torque $$	au in a $$torsional pendulum, analogous to Hooke’s Law?

Accepted Answer

$$	au = -k	heta$$

Question 13

A mass attached to a spring oscillates with displacement $$x = A \cos(\omega t). $$What is the velocity as a function of time?

Accepted Answer

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

Question 14

If a material is stretched beyond its elastic limit, which of the following best describes its behavior?

Accepted Answer

It will no longer obey Hooke’s Law and may break or deform permanently.

Question 15

Which of the following is true about the period $$T of a $$mass-spring system?

Accepted Answer

It is independent of the amplitude of oscillation.

Question 16

A collision occurs between a moving block and a stationary block attached to a spring. Which conservation law(s) must be applied to analyze the system after the collision?

Accepted Answer

Conservation of momentum for the collision and conservation of energy for the spring motion

Question 17

Which of the following best describes the motion of a mass attached to a spring on a frictionless surface after being stretched and released?

Accepted Answer

It oscillates about the equilibrium position with simple harmonic motion.

Question 18

Which of the following is the correct expression for the acceleration of a mass in simple harmonic motion?

Accepted Answer

$$a = -\$$omega^2$$ x$$

Question 19

A $$2\ \mathrm{kg}$$ mass attached to a spring ($$k = 2500\ \mathrm{N/m}) is at$$ $$x = -0.05\ \mathrm{m}$$ during its motion. What is the total mechanical energy of the system?

Accepted Answer

$$E = \frac{1}{2}kx^2$ = \frac{1}{2} 	imes 2500 	imes (0.05)^2$ = 3.125\ \mathrm{J}$$

Spring Force and Hooke’s Law: Physics Study Notes

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