It took 1800J of work to stretch a spring from its natural length of 2m to a length of 5m. Find the spring's force constant.
W = F*d = F * (5-2) = 1800 Joules.
3F = 1800
F = 600 N.
k = 600N./3m = 200N/m
To find the spring's force constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law equation: F = -kx
Where:
F = force exerted by the spring (in Newtons)
k = spring constant (in N/m)
x = displacement of the spring from its equilibrium position (in meters)
In this problem, we know the work done on the spring (1800J) and the displacement of the spring (from 2m to 5m). We can use the formula for work to calculate the force exerted by the spring and then use Hooke's Law to find the spring constant.
1. Calculate the force exerted by the spring:
Work = Force * Displacement
1800J = F * (5m - 2m)
1800J = F * 3m
Divide both sides of the equation by 3m to solve for F:
F = 1800J / 3m
F = 600N
2. Now, use Hooke's Law to find the spring constant:
F = -kx
600N = -k * (5m - 2m)
600N = -k * 3m
Divide both sides of the equation by 3m to solve for k:
k = -600N / (3m)
k = -200N/m
So, the spring constant is -200 N/m.
Note: The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement.