The force required to stretch a Hooke's-law spring varies from 0 N to 76.4 N as we stretch the spring by moving one end 7.46 cm from its unstressed position.
Find the force constant of the spring.
Answer in units of N/m.
Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, this can be expressed as:
F = -kx
Where F is the force applied to the spring, k is the force constant (also known as the spring constant), and x is the displacement of the spring.
In this case, the force required to stretch the spring is given as 0 N to 76.4 N, and the displacement of the spring is 7.46 cm.
At the maximum force of 76.4 N, the displacement x is 7.46 cm. Plugging these values into the equation, we have:
76.4 N = -k(0.0746 m)
Simplifying the equation:
k = -76.4 N / -0.0746 m
The negative signs cancel out, and we are left with:
k = 76.4 N / 0.0746 m
Calculating this:
k ≈ 1024.933 N/m
Therefore, the force constant (or spring constant) of the spring is approximately 1024.933 N/m.