Question 1

A block of mass $$m is $$attached to a spring with force constant $$k$$ and is displaced by a distance $$x$$ from its equilibrium position. What is the restoring force acting on the block according to Hooke's Law?

Accepted Answer

$$F = -kx$$

Question 2

Which of the following best describes the potential energy stored in a stretched or compressed spring?

Accepted Answer

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

Question 3

Two springs with force constants $$k_1$$ and $$k_2$$ are connected in series. What is the equivalent spring constant $$k_{eq}$$?

Accepted Answer

$$k_{eq} = \frac{k_1$ k_2$}{k_1$ + k_2$}$$

Question 4

If two springs with force constants $$k_1$$ and $$k_2$$ are connected in parallel, what is the equivalent spring constant $$k_{eq}$$?

Accepted Answer

$$k_{eq} = k_1$ + k_2$

Question 5

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 6

A spring is stretched by a force $$F$$ and the extension produced is $$x. If $$the same force is applied to a spring with half the spring constant, what will be the new extension?

Accepted Answer

$$2x$$

Question 7

Which of the following statements is true for the work done in stretching a spring from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \frac{1}{2}k(x_2$^2 - x_1$^2)$$

Question 8

A system consists of three identical springs, each with spring constant $$k$$, connected in parallel. What is the equivalent spring constant?

Accepted Answer

$$k_{eq} = 3k$$

Question 9

If a spring is compressed by a distance $$x$$, what is the direction of the restoring force?

Accepted Answer

Opposite to the direction of compression

Question 10

A block is attached to two springs in series with spring constants $$k_1$$ and $$k_2. If a $$force $$F is $$applied, what is the total extension $$x$$?

Accepted Answer

$$x = F\left(\frac{1}{k_1$} + \frac{1}{k_2$}\right)$$

Question 11

Which of the following is NOT a correct assumption for Hooke's Law to be valid?

Accepted Answer

The spring is permanently deformed

Question 12

A spring is cut into two equal halves. What happens to the spring constant of each half?

Accepted Answer

It doubles

Question 13

If a force $$F is $$applied to a spring and it stretches by $$x$$, what is the value of the spring constant $$k$$?

Accepted Answer

$$k = F/x$$

Question 14

A mass $$m is $$attached to a spring and oscillates with period $$T. $$What is the expression for $$T$$?

Accepted Answer

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

Question 15

Which of the following best describes the energy transformation in a mass-spring system undergoing simple harmonic motion?

Accepted Answer

Potential energy is maximum at the extreme positions and kinetic energy is maximum at the equilibrium position

Question 16

If $$n$$ identical springs, each with spring constant $$k$$, are connected in parallel, what is the equivalent spring constant?

Accepted Answer

$$k_{eq} = nk$$

Question 17

A spring is stretched by $$x_1$$ under force $$F_1$$ and by $$x_2$$ under force $$F_2. $$What is the ratio $$F_1$$/$$F_2$$?

Accepted Answer

$$F_1$$/$$F_2$$ = $$x_1$$/$$x_2$$

Question 18

Which of the following is a real-world application of Hooke's Law?

Accepted Answer

Measuring force using a spring balance

Question 19

A spring with spring constant $$k is $$compressed by $$x. $$What is the work done by the spring during this compression?

Accepted Answer

$$W = -\frac{1}{2}kx^2$

Springs, Hooke’s Law, and Series/Parallel Combinations

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