The force exerted by a spring is given by Hooke's Law, which states that the force (F) needed to extend or compress a spring by some distance x is proportional to that distance. That is:

F = kx

where:
- F is the force in newtons,
- x is the distance in meters, and
- k is the spring constant in newtons per meter.

From the problem, we know that a force of +20 newtons stretches the spring 0.40 meters. So we can solve for the spring constant k as follows:

20 N = k * 0.40 m
k = 20 N / 0.40 m
k = 50 N/m

Now, we want to find the force needed to compress the spring by 0.25 meters. We can use Hooke's Law again, but this time we plug in the values for k and x:

F = kx
F = 50 N/m * 0.25 m
F = 12.5 N

So, the force needed to compress the spring by 0.25 meters is 12.5 newtons. Note that the force is negative because it is in the opposite direction of the positive direction defined in the problem.

Question

The force exerted by a spring is given by Hooke's Law, which states that the force (F) needed to extend or compress a spring by some distance x is proportional to that distance. That is:

F = kx

where:
- F is the force in newtons,
- x is the distance in meters, and
- k is the spring constant in newtons per meter.

From the problem, we know that a force of +20 newtons stretches the spring 0.40 meters. So we can solve for the spring constant k as follows:

20 N = k * 0.40 m
k = 20 N / 0.40 m
k = 50 N/m

Now, we want to find the force needed to compress the spring by 0.25 meters. We can use Hooke's Law again, but this time we plug in the values for k and x:

F = kx
F = 50 N/m * 0.25 m
F = 12.5 N

So, the force needed to compress the spring by 0.25 meters is 12.5 newtons. Note that the force is negative because it is in the opposite direction of the positive direction defined in the problem.

Knowee AI · Accepted Answer

The force exerted by a spring is given by Hooke's Law, which states that the force (F) needed to extend or compress a spring by some distance x is proportional to that distance. That is:

F = kx

where:
- F is the force in newtons,
- x is the distance in meters, and
- k is the spring constant in newtons per meter.

From the problem, we know that a force of +20 newtons stretches the spring 0.40 meters. So we can solve for the spring constant k as follows:

20 N = k * 0.40 m
k = 20 N / 0.40 m
k = 50 N/m

Now, we want to find the force needed to compress the spring by 0.25 meters. We can use Hooke's Law again, but this time we plug in the values for k and x:

F = kx
F = 50 N/m * 0.25 m
F = 12.5 N

So, the force needed to compress the spring by 0.25 meters is 12.5 newtons. Note that the force is negative because it is in the opposite direction of the positive direction defined in the problem.

A spring is stretched 0.40 meters in the positive direction by a force of +20 newtons. What is the correct expression for calculating the force needed to compress this spring by 0.25 meters?

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