How Do You Calculate Velocity Loss Due to Friction on a Loop-de-Loop Track?

[reesespieces2]

Homework Statement

If you had a track that was in the shape of a loop-de-loop and you send a small brass ball down the track, how would you calculate how much velocity is lost due to friction?
The radius of the loop is .15m.

Homework Equations

V = (2πr)/[tex]\sqrt{}(4(\pi^2)r)/g[/tex]

The Attempt at a Solution

I don't know what equation to use to find the loss of velocity due to friction so I'm not sure how to go about solving the problem.

 

[anathema]

Hello,

To calculate the loss of velocity due to friction, you can use the concept of conservation of energy. The total mechanical energy of the ball at the top of the loop-de-loop (where it has only potential energy) should equal the total mechanical energy at the bottom of the loop (where it has both potential and kinetic energy).

The initial potential energy at the top of the loop can be calculated using the mass of the ball, the acceleration due to gravity, and the height of the loop. This will give you the initial potential energy (PEi).

At the bottom of the loop, the ball will have both potential and kinetic energy. The final potential energy (PEf) can be calculated using the mass of the ball, the acceleration due to gravity, and the radius of the loop. The final kinetic energy (KEf) can be calculated using the mass of the ball and the velocity at the bottom of the loop (which can be found using the equation you provided).

Since energy is conserved, the initial potential energy (PEi) should equal the sum of the final potential energy (PEf) and final kinetic energy (KEf). You can rearrange this equation to solve for the velocity at the bottom of the loop (Vf).

Once you have the velocity at the bottom of the loop, you can compare it to the initial velocity (Vi) (which can be calculated using the equation you provided) to find the loss of velocity due to friction. The difference between the two velocities will give you the amount of velocity lost due to friction.

I hope this helps! Let me know if you have any further questions.