A hand exerciser utilizes a coiled spring. A force of 87.2 N is required to compress the spring by 0.0232 m. Determine the force needed to compress the spring by 0.0479 m.
We can use Hooke's Law to solve this problem. Hooke's Law states that the force required to compress or extend a spring is directly proportional to the displacement from its equilibrium position.
We are given the force required to compress the spring by 0.0232 m, which is 87.2 N. Let's call this force F1 and displacement x1.
We are asked to determine the force needed to compress the spring by 0.0479 m. Let's call this force F2 and displacement x2.
Hooke's Law can be written as:
F = k * x
Where F is the force, k is the spring constant, and x is the displacement.
Since we know F1 and x1, we can write an equation for them:
87.2 N = k * 0.0232 m
Solving for k, we find:
k = 87.2 N / 0.0232 m ≈ 3765.52 N/m
Now we can use the same equation to find F2:
F2 = k * x2
Plugging in the values we have:
F2 = 3765.52 N/m * 0.0479 m
Calculating this, we find:
F2 ≈ 180.29 N
Therefore, the force needed to compress the spring by 0.0479 m is approximately 180.29 N.