Question

A force of 7 N is applied to a spring. The spring extends by 0.2 m. Calculate the spring constant of the spring.

Given: Force =
Extension =
Spring constant =
Equation:
Calculations:​

Answer 1

Using Hooke's Law, the spring constant of the spring is calculated to be 35 N/m, as a 7 N force causes a 0.2 m extension.

Step-by-step explanation:

To calculate the spring constant of the spring, we can use Hooke's Law, which states that the force F exerted by a spring is directly proportional to the displacement x it undergoes from its equilibrium position, mathematically expressed as F = kx. Here, k is the spring constant we want to find. Given that a force of 7 N extends the spring by 0.2 m, we can rearrange the equation to solve for k: k = F/x.

Calculations:
k = 7 N / 0.2 m
k = 35 N/m

Answer 2

A

(a) 16J

B

(b) 8J

C

(c) 32J

D

(d) 24J

Answer

B

Solution

Small amount of work done in extending the spring by dx is

dW=kxdx

∴W=k∫

0.15

0.05

xdx=

800

2

[(0.15)2-(0.05)2]=8J