A spring of force constant 1500N/M is acted upon by a constant force of 75N.Calculate the potential energy stored in the spring.
To calculate the potential energy stored in a spring, you can use the formula:
Potential energy (PE) = (1/2) * k * x^2
where:
- PE is the potential energy stored in the spring
- k is the force constant of the spring
- x is the displacement of the spring from its equilibrium position.
In this case, the force constant of the spring (k) is given as 1500 N/m, and the constant force (F) acting on the spring is 75 N. To find the displacement (x), we can use Hooke's Law:
F = k * x
Rearrange the equation to solve for x:
x = F / k
Substitute the given values:
x = 75 N / 1500 N/m
x = 0.05 m
Now, substitute the values of k and x into the formula for potential energy:
PE = (1/2) * k * x^2
PE = (1/2) * 1500 N/m * (0.05 m)^2
Calculate the potential energy:
PE = (1/2) * 1500 N/m * 0.0025 m^2
PE = 1.875 J
Therefore, the potential energy stored in the spring is 1.875 Joules.
To calculate the potential energy stored in a spring, you need to use the formula:
Potential Energy = (1/2) * k * x^2
where:
k is the force constant of the spring (in N/m)
x is the displacement from the equilibrium position (in meters)
In this case, the force constant of the spring is given as 1500 N/m. However, the displacement (x) is not provided directly in the question. We can use the given information to determine the displacement though.
The force applied on the spring is 75 N, which means it should cause some displacement. The relationship between force and displacement for a spring is given by Hooke's Law:
F = -k * x
where:
F is the applied force (in N)
k is the force constant of the spring (in N/m)
x is the displacement from the equilibrium position (in meters)
Rearranging the equation, we get:
x = -F / k
Substituting the values, we have:
x = -75 N / 1500 N/m
x = -0.05 m
Since the value of x is negative, it indicates that the displacement is in the opposite direction to the applied force. However, in the formula for potential energy, x is squared, so the negative sign doesn't matter.
Now, we can calculate the potential energy:
Potential Energy = (1/2) * k * x^2
Potential Energy = (1/2) * 1500 N/m * (-0.05 m)^2
Potential Energy = 18.75 joules
Therefore, the potential energy stored in the spring is 18.75 joules.