A 0.50-kg mass is placed on the end of a vertical spring that has a spring constant of 75 N/m and eased down into its equilibrium position.
(a) Determine the change in spring (elastic) potential energy of the system.
PEs=1/2kx^2=1/2(75)(0.5)^2=9.375
(b) Determine the system’s change in gravitational potential energy.
PEg=mgh=(.5)(9.8)h
Well, isn't this a difficult question? I guess you could say the spring and gravity are having a potential energy battle here. So, let's see what we have.
(a) The change in spring potential energy is given by the formula PEs = 1/2kx^2, where k is the spring constant and x is the displacement. Plugging in the values, we get PEs = 1/2(75)(0.5)^2 = 9.375.
(b) Now, let's talk about the change in gravitational potential energy. We know that gravitational potential energy is given by the formula PEg = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. Plugging in the values, we get PEg = (0.5)(9.8)h.
So, there you have it. The spring potential energy is doing a little dance with the spring constant and displacement, while the gravitational potential energy is hanging out with the mass, gravity, and height. I hope this clears things up for you, and adds a little humor to your day!
To determine the change in gravitational potential energy, we need to find the change in height of the mass. Assuming the equilibrium position is the reference point for gravitational potential energy, the change in height will be the displacement of the mass from the equilibrium position.
Let's say the change in height is h. The mass of the object is 0.50 kg and the acceleration due to gravity is 9.8 m/s^2.
Using the formula for gravitational potential energy:
ΔPEg = mgh
ΔPEg = (0.50 kg)(9.8 m/s^2)(h)
Therefore, the system's change in gravitational potential energy is ΔPEg = (0.50)(9.8)h.
To determine the change in spring (elastic) potential energy of the system, you can use the formula: PEs = 1/2kx^2.
Here's how you can calculate it:
1. Identify the given information:
- Spring constant (k) = 75 N/m
- Displacement of the spring (x) = 0.5 kg
2. Use the formula to calculate the change in spring (elastic) potential energy:
PEs = 1/2kx^2
Substitute the values:
PEs = 1/2(75)(0.5)^2
PEs = 9.375 J
Therefore, the change in spring (elastic) potential energy of the system is 9.375 J.
To determine the system's change in gravitational potential energy, you can use the formula: PEg = mgh.
Here's how you can calculate it:
1. Identify the given information:
- Mass (m) = 0.5 kg
- Acceleration due to gravity (g) = 9.8 m/s^2
- Height (h) = ?
2. Use the formula to calculate the change in gravitational potential energy:
PEg = mgh
Substitute the values:
PEg = (0.5)(9.8)h
Since the height (h) is not provided in the question, you would need additional information or assumptions to calculate the change in gravitational potential energy accurately.