A force of 255 Newtons stretches a spring 20 centimeters. How much work is done in stretching the spring from 10 centimeters to 40 centimeters?
A) 97.625000 joules
B) 100.625000 joules
C) 95.625000 joules
D) 90.625000 joules
E) 105.625000 joules

Question

Quizplus · Accepted Answer

The work done on a spring can be calculated using the formula $W = \frac{1}{2} k x^2$, where $W$ is the work done, $k$ is the spring constant, and $x$ is the displacement of the spring from its equilibrium position. First, we need to find the spring constant $k$. Given that a force of 255 Newtons stretches the spring 20 centimeters (0.2 meters), we can use Hooke's Law, $F = kx$, to find $k$. Rearranging for $k$, we get $k = \frac{F}{x} = \frac{255}{0.2} = 1275 \, \text{N/m}$.To find the work done in stretching the spring from 10 cm (0.1 m) to 40 cm (0.4 m), we calculate the work done to stretch it to 40 cm and subtract the work done to stretch it to 10 cm:$$W = \frac{1}{2} k (x_2^2 - x_1^2)$$$$W = \frac{1}{2} \times 1275 \times (0.4^2 - 0.1^2)$$$$W = \frac{1}{2} \times 1275 \times (0.16 - 0.01)$$$$W = \frac{1}{2} \times 1275 \times 0.15$$$$W = 637.5 \times 0.15$$$$W = 95.625 \, \text{joules}$$

A Force of 255 Newtons Stretches a Spring 20 Centimeters