A force of 7.5N stretches a certain spring by 5cm. How much work is done in stretching this spring by 8.0cm

Answer 1

To find the work done in stretching the spring by 8.0 cm, we first need to calculate the spring constant of the spring using the given force and initial displacement.

We know that the force applied is 7.5 N and the initial displacement is 5 cm. Using Hooke's Law equation:

F = kx

Where:
F = force applied (7.5 N)
k = spring constant
x = displacement (5 cm)

Rearranging the equation to solve for k:

k = F / x
k = 7.5 N / 0.05 m
k = 150 N/m

Now that we have the spring constant, we can calculate the work done in stretching the spring by 8.0 cm. The work done in stretching a spring is given by:

W = (1/2)kx^2

Where:
W = work done
k = spring constant (150 N/m)
x = final displacement (8.0 cm or 0.08 m)

W = (1/2)(150 N/m)(0.08 m)^2
W = (1/2)(150 N/m)(0.0064 m)
W = 0.48 J

Therefore, the work done in stretching the spring by 8.0 cm is 0.48 Joules.