Conservation of Kinetic Energy

[appletothecor]

How do I analyze the efficiency of a magnetic bumper other than measuring the velocity and using KE = 1/2 mv^2 to find the final and initial velocities and use that to find a fraction that tells me their relative efficiencies? I am supposed to be able to do so using an inclined track and a meter stick (assumably with the bumper at the bottom).

Also, what would the relative efficiencies be in these three collisions:

moving cart hits a stationary cart
(1) moving cart weighs more than stationary cart
(2) stationary cart weighs more than moving cart
(3) both weigh the same

Not just answers, but the logic behind it too please - thanks!

 

[Curl]

You are not understanding what causes "inefficiency".
It has nothing to do directly with the weight, it is more about the material and the total energy exchanged during the collision (because the "damping" is nonlinear).

 

[appletothecor]

So would the efficiency be the same for all three weight situations?

 

[sophiecentaur]

It's Momentum (mv) that is the conserved quantity. Calculations should be done using that. The KE can be calculated once you have found the velocities - giving you the lost energy.

btw, if you are trying to 'talk Physics' then use the term Mass and not Weight in this context. This is not just being picky. One day it could save your Scientific life.

But a strong enough magnetic bumper wouldn't necessarily dissipate any energy at all so it wouldn't be much help in many impact situations.

 

[appletothecor]

What is the significance of being able to do the momentum calculations on an incline instead of a flat track? Are the calculations done any differently?

 

[sophiecentaur]

Any track you like. You still need to be working things out using Momentum. This supposes that you have enough data to produce an answer.

 

[uart]

What is the significance of being able to do the momentum calculations on an incline instead of a flat track? Are the calculations done any differently?

You do the theoretical calculations using momentum as described above.

You can get experimental results using the inclined track and meter stick to find the initial and final potential energies and relate these to the approximate pre-crash and post-crash KE's.

 

[sophiecentaur]

I am not sure whether this is enough, uart. Where can one place a 'stationary mass' on an inclined plane in such a way that it will satisfy the requirements of this experiment. You would need a 'half pipe' sort of track, with the stationary mass resting at the bottom, I think. That way you could measure the relative proportions of energy before and after. (From the heights reached etc)

 

[uart]

I am not sure whether this is enough, uart. Where can one place a 'stationary mass' on an inclined plane in such a way that it will satisfy the requirements of this experiment. You would need a 'half pipe' sort of track, with the stationary mass resting at the bottom, I think. That way you could measure the relative proportions of energy before and after. (From the heights reached etc)

Yeah something like a "half pipe" was what I had in mind, a decline then flat then incline. I know the OP didn't exactly give that info but I was just guessing that may have been what op meant by "inclined track", since they are talking about doing it with just the track and a meter stick.

 

[sophiecentaur]

Right. Any shape would do - as long as the friction can be kept low enough. The heights reached would be the same, whatever profile.