calculate the energy stored in a stretched spring constant 10000Nm-1(newton per metre)when a force of 200N is applied to it's end?
energy= 1/2 k x^2=1/2 (k)(f/k)^2=1/2 (200^2)(1e4)
To calculate the energy stored in a stretched spring, 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 equation is given by:
F = k * x
Where:
F = Force applied (in N)
k = Spring constant (in N/m)
x = Displacement (in m)
In this case, we have:
F = 200 N
k = 10000 N/m
To find the displacement (x), we need rearrange the equation to solve for x:
x = F / k
Substituting the given values:
x = 200 N / 10000 N/m
x = 0.02 m (or 2 cm)
The energy stored in a stretched spring can be calculated using the formula:
E = (1/2) * k * x^2
Substituting the given values:
E = (1/2) * 10000 N/m * (0.02 m)^2
E = 10 J (Joules)
Therefore, the energy stored in the stretched spring is 10 Joules.