A force of 265 Newtons stretches a spring 20 centimeters. How much work is done in stretching the spring from 15 centimeters to 25 centimeters?
A) 28.5 joules
B) 31.5 joules
C) 26.5 joules
D) 21.5 joules
E) 36.5 joules

Question

Quizplus · Accepted Answer

The work done on the 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 265 Newtons stretches the spring 20 centimeters (0.2 meters), we can use Hooke's Law, $F = kx$, to find $k$. Thus, $k = \frac{F}{x} = \frac{265}{0.2} = 1325 \, \text{N/m}$.To find the work done in stretching the spring from 15 cm (0.15 m) to 25 cm (0.25 m), we calculate the work done to stretch it to 25 cm and subtract the work done to stretch it to 15 cm:$$W = \frac{1}{2} k (x_2^2 - x_1^2)$$$$W = \frac{1}{2} \times 1325 \times (0.25^2 - 0.15^2) = \frac{1}{2} \times 1325 \times (0.0625 - 0.0225) = 662.5 \times 0.04 = 26.5 \, \text{joules}$$

A Force of 265 Newtons Stretches a Spring 20 Centimeters