Q: Which equation correctly represents the vector form of Hooke's Law?

$$\vec{F}_{\text{elastic}} = -k\vec{x}$$

Question 1

According to Hooke's Law, what is the mathematical relationship between the force exerted by a spring and its displacement from equilibrium?

Accepted Answer

$$F_{	ext{elastic}} = -kx$$

Question 2

A spring with a spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.05\ \mathrm{m}. $$What is the magnitude of the force exerted by the spring?

Accepted Answer

$$F = 10\ \mathrm{N}$$

Question 3

Which of the following factors does NOT affect the spring constant $$k of a $$spring?

Accepted Answer

The mass attached to the spring

Question 4

If a spring is stretched so that its displacement is doubled, what happens to the force it exerts according to Hooke's Law?

Accepted Answer

The force is doubled

Question 5

What is the SI unit of the spring constant $$k$$?

Accepted Answer

$$\mathrm{N/m}$$

Question 6

A student claims that a stiffer spring has a smaller spring constant $$k. Is $$this correct? Why or why not?

Accepted Answer

No, because a stiffer spring has a larger $$k$$

Question 7

Which of the following best describes the microscopic origin of friction between two solid surfaces?

Accepted Answer

Friction arises from attractive and repulsive forces at microscopic contact points

Question 8

In the context of friction, what is the role of 'microscopic contact points' between two surfaces?

Accepted Answer

They are regions where intermolecular forces act, contributing to friction

Question 9

A block is sliding on a surface. According to the physical explanation of friction, what type of forces act at the microscopic contact points?

Accepted Answer

Both attractive and repulsive forces

Question 10

If the number of microscopic contact points between two surfaces increases, what is the expected effect on the frictional force?

Accepted Answer

The frictional force increases

Question 11

A spring is stretched by $$0.1\ \mathrm{m}$$ and exerts a force of $$5\ \mathrm{N}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = 50\ \mathrm{N/m}$$

Question 12

Which of the following real-world scenarios best illustrates Hooke's Law?

Accepted Answer

A rubber band stretching when a weight is attached

Question 13

A spring is cut in half. How does the spring constant $$k of $$each half compare to the original spring?

Accepted Answer

Each half has twice the $$k of $$the original

Question 14

Which equation correctly represents the vector form of Hooke's Law?

Accepted Answer

$$\vec{F}_{	ext{elastic}} = -k\vec{x}$$

Question 15

A block is at rest on a horizontal surface. Which of the following best explains why it does not move, according to the microscopic explanation of friction?

Accepted Answer

Microscopic contact points create forces that resist motion

Question 16

If the diameter of a spring is increased while keeping all other factors constant, what happens to the spring constant $$k$$?

Accepted Answer

$$k$$ increases

Question 17

Which of the following statements about friction is correct?

Accepted Answer

Friction is a result of both attractive and repulsive forces at microscopic contact points

Question 18

A spring with a spring constant $$k is $$stretched by a distance $$x. $$What is the work done by the spring force as it returns to its equilibrium position?

Accepted Answer

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

Question 19

Which of the following would most likely increase the frictional force between two surfaces?

Accepted Answer

Increasing the normal force pressing the surfaces together

Study Notes: Hooke's Law and Physical Explanation of Friction

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