the potential energy of a spring is 0.3 J when it is compressed 0.04 m to the left of its equilibrium position. At this point it comes to its leftmost position. What is its kinetic energy when it returns to the equilibrium point
To find the kinetic energy of the spring when it returns to the equilibrium point, we need to understand the relationship between potential energy and kinetic energy.
In the case of a spring, potential energy is stored in it when it is compressed or stretched. This potential energy can be converted into kinetic energy when the spring is released.
The potential energy of a spring can be calculated using the equation:
PE = (1/2) k x²
Where:
PE is the potential energy of the spring
k is the spring constant
x is the displacement of the spring from its equilibrium position
In this case, the potential energy is given as 0.3 J and the displacement is -0.04 m (since it is compressed to the left).
0.3 J = (1/2) k (-0.04 m)²
Simplifying the equation, we get:
0.3 J = (1/2) k (0.0016 m²)
Now, let's solve for the spring constant, k:
k = (0.3 J) / (0.0016 m²)
k ≈ 187.5 N/m
Now that we know the spring constant, we can find the kinetic energy when the spring returns to the equilibrium point.
The total mechanical energy of the system is conserved, which means that the sum of the potential energy and kinetic energy remains constant. At the equilibrium point, all the potential energy is converted into kinetic energy.
Thus, when the spring returns to the equilibrium point, the potential energy is zero, and all the initial potential energy is transformed into kinetic energy.
Therefore, the kinetic energy of the spring when it returns to the equilibrium point is 0.3 J.