A hand exerciser utilizes a coiled spring. A force of 86.9 N is required to compress the spring by 0.0231 m. Determine the force needed to compress the spring by 0.0432 m.
F₁=kx₁
F₂=kx₂
F₁/F₂=x₁/x₂
F₂=F₁x₂/x₁
To determine the force needed to compress the spring by 0.0432 m, we can use Hooke's Law, which states that the force needed to compress or extend a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law is mathematically represented as:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant (a measure of the stiffness of the spring),
and x is the displacement of the spring from its equilibrium position.
To find the force needed to compress the spring by 0.0432 m, we first need to find the spring constant, k.
The formula to calculate the spring constant is:
k = F / x
Given that a force of 86.9 N is required to compress the spring by 0.0231 m, we can substitute the values into the equation:
k = 86.9 N / 0.0231 m
k = 3767.93 N/m (rounded to 2 decimal places)
Now that we have the spring constant, we can calculate the force needed to compress the spring by 0.0432 m using Hooke's Law:
F = k * x
F = 3767.93 N/m * 0.0432 m
F = 162.64 N (rounded to 2 decimal places)
Therefore, the force needed to compress the spring by 0.0432 m is approximately 162.64 N.