Question 1

According to Hooke's Law, what is the mathematical relationship between the restoring force $$F_{elastic}$$ and the displacement $$x$$ from equilibrium for a spring?

Accepted Answer

$$F_{elastic} = -kx$$

Question 2

Which of the following best describes the physical origin of friction at the microscopic level, as shown in the diagram?

Accepted Answer

Friction arises from the electrical attractive and repulsive forces at microscopic contact points between surfaces.

Question 3

The spring constant $$k is a $$measure of:

Accepted Answer

The stiffness of the spring.

Question 4

Which of the following changes would increase the spring constant $$k of a $$spring?

Accepted Answer

Decreasing the diameter of the wire.

Question 5

A spring is stretched by $$0.2\ \mathrm{m}$$ and exerts a force of $$10\ \mathrm{N}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = 20\ \mathrm{N/m}$$

Question 6

If the force applied to a spring is doubled, what happens to the displacement $$x$$ according to Hooke's Law?

Accepted Answer

It is doubled.

Question 7

Which SI unit is used for the spring constant $$k$$?

Accepted Answer

$$\mathrm{N/m}$$

Question 8

A block is sliding on a surface. According to the microscopic model, why does friction oppose the motion?

Accepted Answer

Because of attractive and repulsive forces at microscopic contact points.

Question 9

Which of the following statements about Hooke's Law is correct?

Accepted Answer

It is valid only within the elastic limit of the material.

Question 10

A spring with a spring constant $$k = 100\ \mathrm{N/m} is $$compressed by $$0.05\ \mathrm{m}. $$What is the magnitude of the force exerted by the spring?

Accepted Answer

$$2.5\ \mathrm{N}$$

Question 11

Which factor does NOT affect the value of the spring constant $$k$$?

Accepted Answer

The color of the spring.

Question 12

If a spring is cut in half, what happens to its spring constant $$k$$?

Accepted Answer

It is doubled.

Question 13

Which of the following best explains why stiffer springs have a higher spring constant $$k$$?

Accepted Answer

They require more force to produce the same displacement.

Question 14

A force vs. displacement graph for a spring is a straight line. What does the slope of this line represent?

Accepted Answer

The spring constant $$k.$$

Question 15

Which of the following is a correct vector form of Hooke's Law?

Accepted Answer

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

Forces in Mechanics: Hooke’s Law and Friction

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