Perform the following steps for each scenario listed below: - Try to make an int
ID: 1522698 • Letter: P
Question
Perform the following steps for each scenario listed below:
- Try to make an intuitive physical argument for whether or not the total mechanical energy is conserved in the system
- If you think mechanical energy is conserved, try to prove it by mathematically verifying that the net work done by non-conservative forces is zero
- If you think mechanical energy is not conserved, try to prove it by computing the total mechanical energy at different points in time and showing that they're nor the same, and try to determine where the non-conservative work is coming from. (Hint: Are there types of energy other than mechanical energy?)
Scenarios:
1. The system: the pair of blocks in an Atwood's Machine. The pulley and rope are massless, and the pulley has a frictionless axle. One mass is larger than the other so one mass rises and the other falls.
2. The system: a piece of clay. At the initial time, the clay is flying towards a wall, at the final time, the clay is stuck to the wall.
3. The system:a piece of clay and Nancy. At the inital time, Nancy is ice skating and a piece of clay is flying towards him. At the final time, the clay has struck Nancy and sticks to her head.
4. The system: a ball and a massless spring. At the initial time, the ball is dropped above the spring. At the final time, the ball has come to a halt and the spring is compressed.
5. The system: a rocket taking off. At the initial time, the rocket is sitting on the ground, filled with fuel. At the final time, the fuel has ignited, and the rocket is moving upward.
Explanation / Answer
1) Here, the total mechanical energy is conserved in the system .
=> Work done by tension in rope = Gain in kinetic energy of mass
2) Here, the total mechanical energy is not conserved in the system .
=> Initial time total energy of clay = kinetic energy
=> Final time kinetic energy of clay = 0
3) Here, the total mechanical energy is conserved in the system .
=> Initial energy of system = kinetic energy of clay + kinetic energy of Nancy
=> Final energy of system = Final kinetic energy of ( Nancy + clay ) .
4) Here, the total mechanical energy is conserved in the system .
=> Initial energy of system = total gravitational potential energy of ball .
=> Final energy of system = elastic potential energy stored in spring .
5) Here, the total mechanical energy is not conserved in the system .
=> Initial time total energy of rocket = zero kinetic energy of rocket .
=> Final time energy of rocket = kinetic enery of rocket .