Conservation of Linear, Rotational Mechanical Energy

[mrshappy0]

Homework Statement

Attached is a photo of the linear and rotational dynamics exercises. Times t1 and t2 were measured. For the linear exercise the top block was pushed with an initial force along the FRICTIONLESS level plane. It passed the timing device twice. Once through and once on the way back. Would the mechanical energy be conserved in this situation? For exercise two the disk was held at rest and released. Gravity applied torque at a set radius. The angular velocity was determined for times t0, t1, and t2. The disk was flat (level) with surface. Would mechanical energy be conserved for this?

Homework Equations

ME_rotational=IW²/2

ME_linear=MV²/2

The Attempt at a Solution

My data shows a small change in MEnergy. Does this imply that it is conserved but not perfectly due to air resistance, not perfectly frictionless, etc...

For the second section, I thought mechanical energy was not conserved when an external torque is applied. In this case gravity is applying external torque.

 

[anathema]

Therefore, mechanical energy would not be conserved in this situation.

Thank you for sharing your data and questions regarding the conservation of mechanical energy in these exercises. I would like to offer some insights and explanations to help clarify your understanding.

Firstly, in the linear exercise, it is important to note that the presence of air resistance and friction can cause a small change in mechanical energy. However, in an ideal scenario where these factors are negligible, mechanical energy should be conserved. This means that the initial and final mechanical energy values should be equal. The fact that you observed a small change in mechanical energy could be due to experimental error or the presence of these external factors.

In the second exercise, you are correct in stating that the presence of an external torque, in this case gravity, would result in a change in mechanical energy. This is because external forces or torques can do work on a system, thus changing its mechanical energy. In this situation, the mechanical energy of the disk would decrease as it gains rotational kinetic energy due to the applied torque.

I hope this helps to clarify your understanding of the conservation of mechanical energy in these exercises. It is important to consider all factors and sources of error when analyzing experimental data. Keep up the good work in your scientific studies!