To solve this problem, we need to use Hooke's Law, which states that the force needed to extend or compress a spring by some distance is proportional to that distance. That is:

F = kx

where:
F is the force applied,
k is the spring constant, and
x is the distance the spring is stretched or compressed.

Work is defined as the force applied over a distance, so the work done on the spring can be calculated as:

W = 1/2 kx^2

Given that 6J of work is needed to stretch the spring from its natural length of 32 cm to a length of 50 cm, we can set up the equation:

6 = 1/2 k (50-32)^2

Solving for k, we get:

k = 2*6 / (50-32)^2 = 0.027 J/cm^2

Now, we can calculate the work needed to stretch the spring from 37 cm to 45 cm:

W = 1/2 * 0.027 * (45-37)^2 = 0.216 J

So, approximately 0.22 J of work is needed to stretch the spring from 37 cm to 45 cm.

Question

To solve this problem, we need to use Hooke's Law, which states that the force needed to extend or compress a spring by some distance is proportional to that distance. That is:

F = kx

where:
F is the force applied,
k is the spring constant, and
x is the distance the spring is stretched or compressed.

Work is defined as the force applied over a distance, so the work done on the spring can be calculated as:

W = 1/2 kx^2

Given that 6J of work is needed to stretch the spring from its natural length of 32 cm to a length of 50 cm, we can set up the equation:

6 = 1/2 k (50-32)^2

Solving for k, we get:

k = 2*6 / (50-32)^2 = 0.027 J/cm^2

Now, we can calculate the work needed to stretch the spring from 37 cm to 45 cm:

W = 1/2 * 0.027 * (45-37)^2 = 0.216 J

So, approximately 0.22 J of work is needed to stretch the spring from 37 cm to 45 cm.

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