Elasticity

Question 1

Hooke's law states that within the elastic limit, extension is:

Accepted Answer

Directly proportional to force — Hooke's law: F = kx, so extension is directly proportional to force.

Question 2

The SI unit of the spring constant k is:

Accepted Answer

N m⁻¹ — From k = F / x, the unit is newton per metre (N m⁻¹).

Question 3

A spring extends 0.02 m under a 10 N force. Its spring constant is:

Accepted Answer

500 N m⁻¹ — k = F / x = 10 / 0.02 = 500 N m⁻¹.

Question 4

A spring with k = 300 N m⁻¹ is stretched by 0.10 m. The force applied is:

Accepted Answer

30 N — F = kx = 300 × 0.10 = 30 N.

Question 5

The elastic potential energy stored in a stretched spring is given by:

Accepted Answer

½kx² — Elastic PE = ½kx² = ½Fx, the area under the force–extension graph.

Question 6

Beyond the elastic limit, a spring:

Accepted Answer

Does not return to original length — Past the elastic limit the material is permanently deformed.

Question 7

A spring of k = 400 N m⁻¹ is stretched by 0.05 m. The elastic PE stored is:

Accepted Answer

0.5 J — E = ½kx² = ½ × 400 × (0.05)² = ½ × 400 × 0.0025 = 0.5 J.

Question 8

Two identical springs are connected in series. Compared to one spring, the combination is:

Accepted Answer

Less stiff (smaller k) — Springs in series stretch more for the same force, giving a smaller effective spring constant.

Question 9

A larger spring constant k means the spring is:

Accepted Answer

Stiffer — A large k needs more force per unit extension, i.e. a stiffer spring.

Question 10

On a force–extension graph obeying Hooke's law, the gradient represents the:

Accepted Answer

Spring constant — The gradient of the straight line is F / x = k, the spring constant.