A robot arm expends 15J of work to extend a spring 10cm from its equilibrium position. How much force is required?
energy=1/2 k x^2
15=1/2 k (.1)^2 solve for k.
Force= k *.1
15
To find the force required to extend the spring, we can use Hooke's Law, which states that the force required to extend 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 = Force applied to the spring (in Newtons)
k = Spring constant (in Newtons per meter)
x = Displacement from the equilibrium position (in meters)
In this case, we are given the work done (W) to extend the spring and the displacement (x) from the equilibrium position.
We know that work done is equal to the product of force and displacement:
W = F * x
We can rearrange this equation to solve for force (F):
F = W / x
Now, let's substitute the known values:
W = 15 J (work done)
x = 10 cm = 0.1 m (displacement)
F = 15 J / 0.1 m
F = 150 N
Therefore, the force required to extend the spring is 150 Newtons.