Two joules of energy are required to extend a spring by .25 m. What is the spring constant?
Use the formula E = (1/2) k X^2
E is the energy in joules. k will be in newtons per meter is the extenseion (X) is in meters.
To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement. The formula for Hooke's Law is:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant, and
x is the displacement from the equilibrium position.
In this case, we know the energy required to extend the spring (2 J) and the displacement (0.25 m). However, we need to convert the energy into force so that we can use Hooke's Law.
The formula to convert energy into force is:
E = F * d
Where:
E is the energy,
F is the force, and
d is the distance.
In this case, we have E = 2 J and d = 0.25 m. Rearranging the formula, we can solve for F:
F = E / d
Substituting the given values, we get:
F = 2 J / 0.25 m
F = 8 N
Now we can use Hooke's Law to find the spring constant.
8 N = k * 0.25 m
To isolate k, divide both sides by 0.25 m:
k = 8 N / 0.25 m
k = 32 N/m
Therefore, the spring constant is 32 N/m.