1998 Physics B Rainstick Problem (Help)

[eltono19]

Students are designing an experiment to demonstrate the conversion of mechanical energy to thermal energy. They have designed the apparatus shown above. Small Lead Beads of a total mass M and the specific heat c fill the lower hollow sphere. The valves between spheres and the hollow tube can be opened or closed to control the flow of the lead beads. Initially both valves are open.

A) The lower valve is closed and the student turns the apparatus 180 γ about the horizontal axis, so that the filled sphere is now on top. This elevates the center of mass of the lead beads by a vertical distance h. What minimum amount of work must the student do to accomplish this?

W=f*d
U= Q-W


I honestly have no idea where to start. The lack of actual measurements threw me off so I appreciate any help.

 

[lippyka]

Answer: The minimum amount of work done by the student would be equal to the change in gravitational potential energy of the lead beads, which can be calculated using the equation U = mgh, where m is the total mass of the lead beads, g is the acceleration due to gravity and h is the vertical distance the center of mass was elevated.

 

[tomcue]

I would suggest that the students begin by clearly defining their experimental setup and identifying the variables involved. This includes specifying the mass of the lead beads, the specific heat of the material, and the distance h that the center of mass is elevated. These values are crucial for calculating the work and energy involved in the experiment.

Next, the students should determine the initial and final states of the system. In this case, the initial state is with both valves open and the filled sphere on the bottom, while the final state is with the lower valve closed and the filled sphere on top. The change in position of the center of mass is also important to consider.

Once these parameters are established, the students can use the equations provided (W=fd and U=Q-W) to calculate the minimum amount of work required to elevate the center of mass by a distance h. This work will be equal to the change in potential energy of the system, which can then be used to determine the amount of thermal energy that is generated through the conversion of mechanical energy.

It is also important for the students to consider potential sources of error in their experiment, such as friction or air resistance, and to take steps to minimize these effects. Additionally, they should repeat the experiment multiple times to ensure consistency and accuracy in their results.

In conclusion, as a scientist, I would advise the students to carefully consider all relevant variables, accurately measure and record their data, and use appropriate equations and calculations to determine the minimum amount of work required to elevate the center of mass and demonstrate the conversion of mechanical energy to thermal energy.