A 3.2 kg block is hanging stationary from the end of a vertical spring that is attached to the ceiling and has an elastic potential energy of 1.8 J. What is the elastic potential energy of the system when the 3.2 kg block is replaced by a 5.0 kg block?
answer it please
To find the elastic potential energy of the system when the 3.2 kg block is replaced by a 5.0 kg block, we need to understand the relationship between elastic potential energy and the displacement of the spring.
Elastic potential energy (U) in a spring is given by the equation:
U = (1/2) * k * x^2
Where:
- U is the elastic potential energy
- k is the spring constant (a measure of the stiffness of the spring)
- x is the displacement from the equilibrium position of the spring
In this case, we have the elastic potential energy (U) initially when the 3.2 kg block is attached to the spring, and we want to find the elastic potential energy when the 5.0 kg block is attached.
Let's assume that the displacement (x) remains the same when we replace the block. Since the spring is still attached to the ceiling, the displacement will be determined by the weight of the block, which is the force of gravity acting on it.
First, we can find the displacement (x) for the 3.2 kg block. The weight of an object is given by the equation:
F = m * g
Where:
- F is the weight of the object
- m is the mass of the object
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
For the 3.2 kg block:
F = m * g
F = 3.2 kg * 9.8 m/s^2
F ≈ 31.36 N
Since the block is stationary, the weight is balanced by the force exerted by the spring. The force exerted by the spring is given by Hooke's Law:
F = k * x
Where:
- F is the force exerted by the spring
- k is the spring constant
- x is the displacement
Setting the equations for the weight and the force exerted by the spring equal to each other:
m * g = k * x
Solving for x:
x = (m * g) / k
Now, we can calculate the initial elastic potential energy (U_initial) with the 3.2 kg block:
U_initial = (1/2) * k * x^2
To find the new elastic potential energy (U_new) when the 5.0 kg block is attached, we can use the same displacement (x), calculated with the mass of the 5.0 kg block:
x = (m * g) / k
Finally, we can calculate the elastic potential energy of the system when the 5.0 kg block is attached:
U_new = (1/2) * k * x^2
By following these steps, we can determine the elastic potential energy of the system when the 3.2 kg block is replaced by a 5.0 kg block.