The force required to stretch a Hooke’s-law spring varies from 0 N to 70.4 N as we stretch the spring by moving one end 5.35 cm from its unstressed position.
Find the force constant of the spring. Answer in units of N/m
F = -k*x
where F = force, x is displacement
70.4 = -k*0.0535
To find the force constant of the spring, you can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.
Hooke's Law can be expressed as:
F = k * x
where F is the force, k is the force constant (also known as the spring constant), and x is the displacement.
In the given problem, the force varies from 0 N to 70.4 N, and the displacement is 5.35 cm (which needs to be converted to meters).
Step 1: Convert the displacement from centimeters to meters.
5.35 cm = 0.0535 m
Step 2: Use Hooke's Law to find the force constant.
Since the force varies from 0 N to 70.4 N, we can choose any specific data point within this range. Let's use the maximum force of 70.4 N.
70.4 N = k * 0.0535 m
Step 3: Solve for the force constant, k.
k = 70.4 N / 0.0535 m
Using a calculator, we can find that:
k ≈ 1313.084 N/m
So, the force constant of the spring is approximately 1313.084 N/m.