It takes 5.50 J of work to stretch a spring 5.90 cm from its unstressed length. What is the spring constant k in N/m?
To find the spring constant k, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the force applied to the spring (in Newtons),
k is the spring constant (in N/m),
and x is the displacement of the spring (in meters).
We are given the work done to stretch the spring, which is equal to the potential energy stored in the spring. The potential energy can be calculated using the formula:
Potential Energy = (1/2) * k * x^2
In this case, the work done (W) is equal to the potential energy (PE):
W = PE
So, we have:
W = (1/2) * k * x^2
Now we can solve for the spring constant k. Rearranging the equation, we have:
k = (2 * W) / x^2
Substituting the given values:
W = 5.50 J (Joules)
x = 0.0590 m (converted from 5.90 cm to meters)
Plugging in these values, we get:
k = (2 * 5.50 J) / (0.0590 m)^2
Simplifying the expression, we have:
k = (11 J) / (0.003481 m^2)
Finally, calculating the value of k:
k ≈ 3157.39 N/m
Therefore, the spring constant k is approximately 3157.39 N/m.