A 2.40 kg object is hanging from the end of a vertical spring. The spring constant is 53.0 N/m. The object is pulled 0.200 m downward and released from rest. Complete the table below by calculating the translational kinetic energy, the gravitational potential energy, the elastic potential energy, and the total mechanical energy E for each of the vertical positions indicated. The vertical positions h indicate distances above the point of release, where h = 0.
h(m) KE(J)PE-gravity(J) PE-elastic(J)
0
0.200
0.400
So what is your question about this?
howdo you do it?
it is a table and you have to find the
KE(J) Gravity(J) and PE-elastic(J)
h(m)
0
0.200
0.400
To calculate the different types of energy at each position, we can use the following formulas:
1. Translational Kinetic Energy (KE):
KE = (1/2) * m * v^2
2. Gravitational Potential Energy (PE-gravity):
PE-gravity = m * g * h
3. Elastic Potential Energy (PE-elastic):
PE-elastic = (1/2) * k * x^2
4. Total Mechanical Energy (E):
E = KE + PE-gravity + PE-elastic
Given:
Mass (m) = 2.40 kg
Spring Constant (k) = 53.0 N/m
Distance Pulled (x) = 0.200 m
Gravitational Acceleration (g) = 9.8 m/s^2
Using these formulas, we can calculate the values for each position in the table.
1. At h = 0:
- Translational Kinetic Energy:
The object is released from rest, so its initial velocity is 0.
KE = (1/2) * m * 0^2 = 0 J
- Gravitational Potential Energy:
PE-gravity = m * g * h = 2.40 kg * 9.8 m/s^2 * 0 m = 0 J
- Elastic Potential Energy:
PE-elastic = (1/2) * k * x^2 = (1/2) * 53.0 N/m * (0.200 m)^2 = 0.212 J
- Total Mechanical Energy:
E = KE + PE-gravity + PE-elastic = 0 J + 0 J + 0.212 J = 0.212 J
2. At h = 0.200 m:
- Translational Kinetic Energy:
KE = (1/2) * m * v^2
Since the object is released from rest, its velocity can be calculated using the equation: v = sqrt(2 * g * h)
v = sqrt(2 * 9.8 m/s^2 * 0.200 m) = 2.8 m/s (approximately)
KE = (1/2) * 2.40 kg * (2.8 m/s)^2 = 9.07 J (approximately)
- Gravitational Potential Energy:
PE-gravity = m * g * h = 2.40 kg * 9.8 m/s^2 * 0.200 m = 4.704 J (approximately)
- Elastic Potential Energy:
PE-elastic = (1/2) * k * x^2 = (1/2) * 53.0 N/m * (0.200 m)^2 = 0.212 J
- Total Mechanical Energy:
E = KE + PE-gravity + PE-elastic = 9.07 J + 4.704 J + 0.212 J = 13.986 J (approximately)
3. At h = 0.400 m:
- Translational Kinetic Energy:
v = sqrt(2 * 9.8 m/s^2 * 0.400 m) = 3.9 m/s (approximately)
KE = (1/2) * 2.40 kg * (3.9 m/s)^2 = 18.108 J (approximately)
- Gravitational Potential Energy:
PE-gravity = m * g * h = 2.40 kg * 9.8 m/s^2 * 0.400 m = 9.408 J (approximately)
- Elastic Potential Energy:
PE-elastic = (1/2) * k * x^2 = (1/2) * 53.0 N/m * (0.200 m)^2 = 0.212 J
- Total Mechanical Energy:
E = KE + PE-gravity + PE-elastic = 18.108 J + 9.408 J + 0.212 J = 27.728 J (approximately)
So, the completed table should look like this:
h(m) KE(J) PE-gravity(J) PE-elastic(J) E(J)
0 0 0 0.212 0.212
0.200 9.07 4.704 0.212 13.986
0.400 18.108 9.408 0.212 27.728