A spring of force constant 1500nm is acted upon by a constant force of 45n calculate the potential energy stored in spring?
First, force is in N/m, not Nm. Watch the units -- they are important.
F = kx (note that F = N/m * m = N)
So,
E = 1/2 kx^2 = 1/2 * 1500 * (45/1500)^2
To calculate the potential energy stored in a spring, you can use the formula:
Potential energy (PE) = (1/2) * k * x^2
where:
k is the force constant of the spring
x is the displacement from the equilibrium position of the spring
In this case, the force constant (k) of the spring is given as 1500 N/m, and a constant force of 45 N is acting on the spring.
Since the force acting on the spring is constant, we can find the displacement by dividing the force by the force constant:
Displacement (x) = F / k
Substituting the given values:
Displacement (x) = 45 N / 1500 N/m
= 0.03 m
Now, we can calculate the potential energy stored in the spring:
Potential energy (PE) = (1/2) * k * x^2
= (1/2) * 1500 N/m * (0.03 m)^2
= 6.75 Nm
= 6.75 Joules
Therefore, the potential energy stored in the spring is 6.75 Joules.
To calculate the potential energy stored in a spring, you can use the formula:
Potential Energy = (1/2) * k * x^2
Where:
- k is the force constant (also known as the spring constant)
- x is the displacement of the spring from its equilibrium position
In this case, we are given that the force constant of the spring (k) is 1500 N/m. However, the force acting on the spring (45 N) is not directly related to the calculation of potential energy.
To determine the displacement (x), we need to use the relationship between force and spring constant:
Force = k * x
Since we know the force (45 N) and the spring constant (1500 N/m), we can rearrange the equation to solve for x:
x = Force / k
Plugging in the respective values:
x = 45 N / 1500 N/m = 0.03 m
Now, we can calculate the potential energy:
Potential Energy = (1/2) * k * x^2
Potential Energy = (1/2) * (1500 N/m) * (0.03 m)^2
Potential Energy = 0.675 J
Therefore, the potential energy stored in the spring is 0.675 joules.