A 0.25 kg{\rm kg} object is suspended on a light spring of spring constant 35N/mN/m . The spring is then compressed to a position 17cmcm above the stretched equilibrium position.How much more energy does the system have at the compressed position than at the stretched equilibrium position?
To find the difference in potential energy between the compressed position and the stretched equilibrium position, we need to calculate the potential energy at each position.
The potential energy stored in a spring is given by the formula:
PE = 0.5 * k * x^2
where PE is potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
Given:
Mass of the object (m) = 0.25 kg
Spring constant (k) = 35 N/m
1. Stretched Equilibrium Position:
At the stretched equilibrium position, the displacement (x) is 0. This means the object is not compressed or stretched, and the potential energy is zero.
PE_stretched = 0
2. Compressed Position:
At the compressed position, the displacement (x) is 17 cm = 0.17 m. Now, we can calculate the potential energy at this position.
PE_compressed = 0.5 * k * x^2
= 0.5 * 35 * (0.17^2)
The potential energy at the compressed position can be found by plugging in the values into the equation and calculating.
Now, you can plug in the given values and calculate the potential energy at the compressed position.
PE_compressed = 0.5 * 35 * (0.17^2)
= 0.5 * 35 * 0.0289
= 0.5 * (1.015)
= 0.5075 J
Therefore, the potential energy at the compressed position is 0.5075 J.
To find the difference in potential energy between the compressed position and the stretched equilibrium position, we subtract the potential energy at the stretched equilibrium position from the potential energy at the compressed position.
Difference in potential energy = PE_compressed - PE_stretched
= 0.5075 J - 0 J
= 0.5075 J
Therefore, the system has an additional 0.5075 J of energy at the compressed position compared to the stretched equilibrium position.