Conservation of Energy Question

[homeslice]

Hi, there. I'm doing a correspondance physics course, and this one question has me stumped. I'm calculating the efficiency of a pendulum, and therefore need to find the mechanical energy, as well as the thermal energy. However, I don't think they've given me enough information.

Mass of pendulum bob = 240.3 g
Diameter of pendulum bob = 3.50 cm
Initial height of pendulum bob = 48.0 cm
Length of pendulum string = 2.14 m
Time interval photogate light interruption = 11.8 ms

*The photogate light interruption happens at the lowest point of the pendulum swing.

Thanks for your help,
-Gary

 

[HallsofIvy]

You would certainly need to know the speed of the pendulum at various times- if the pendulum were 100% efficient (no friction) then you could find the speed as a function of time from the given information but to determine the efficiency, you will need to know how it slows down.

 

[homeslice]

Yeah, I know that. My problem is that I can't figure out how to get the speed, because I don't know the distance that the bob has travelled. Is it actually possible to determine the speed with the information that I have?

 

[OlderDan]

Yeah, I know that. My problem is that I can't figure out how to get the speed, because I don't know the distance that the bob has travelled. Is it actually possible to determine the speed with the information that I have?

It's not an ideal situation, but in principle you have been given enough information. You can calculate the change in potential energy of the pendulum based on starting height relative to the bottom and you can calculate the kinetic energy at the first pass through the lowest point of the swing by using the interruption time and bob diameter to find velocity. From this you can find the energy "lost" in the first quarter cycle of the motion, an calculate an efficiency.

It would be better if you could measure velocity for multiple passes, but you have to use what you are given.

 

[homeslice]

How does the diameter of the bob have anything at all to do with the velocity?

 

[OlderDan]

How does the diameter of the bob have anything at all to do with the velocity?

The bob is what interrupts the light beam. The beam is blocked for the time it takes the bob to move one diameter.