Question

Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 42 cm. How much work is needed to stretch the spring from 35 cmto 40 cm?

Answer 1

The work needed to stretch the spring from 35 cm to 40 cm is 1.55 J.

Step-by-step explanation:

To calculate the work needed to stretch the spring from 35 cm to 40 cm, we can first find the work required to stretch the spring from 0 cm to 40 cm and subtract the work required to stretch the spring from 0 cm to 35 cm. In Example 7.5, it is stated that it takes 0.54 J of work to stretch a spring 6 cm from its equilibrium position. Using this information, we can find the spring constant of the spring.

Given:

• Work to stretch from 0 cm to 42 cm = 2 J
• Work to stretch from 0 cm to 30 cm = 0 J
• Length change from 0 cm to 42 cm = 42 cm - 0 cm = 42 cm
• Length change from 0 cm to 30 cm = 30 cm - 0 cm = 30 cm
• Work to stretch from 30 cm to 42 cm = Work to stretch from 0 cm to 42 cm - Work to stretch from 0 cm to 30 cm = 2 J - 0 J = 2 J

Now, we can find the work to stretch from 30 cm to 35 cm and subtract it from the previous result to get the work to stretch from 35 cm to 40 cm.

• Length change from 30 cm to 35 cm = 35 cm - 30 cm = 5 cm
• Work to stretch from 30 cm to 35 cm = (5 cm / 6 cm) * 0.54 J = 0.45 J
• Work to stretch from 35 cm to 40 cm = 2 J - 0.45 J = 1.55 J

Therefore, the work needed to stretch the spring from 35 cm to 40 cm is 1.55 J.