How Does the Coefficient of Friction Affect a Trolley's Motion Down a Ramp?

[physics99]

Hello,

In class we were given the following task:

Analyse the motion of an object rolling down a ramp to determine the coefficient of friction. Use the information obtained and projectile motion analyses to determine the distance a projectile will travel when launched off the end of a ramp.

I know that you can use vector diagrams when a trolley is moving at constant velocity. Then friction would be mg sin Ø But in this case the trolley would be accelerating down the ramp?

If I have a ramp that leads to the floor, I could time the motion from when it leaves the ramp until it stops. Then I can also measure the distance it has travelled. The horizontal acceleration would be 0 m/s^2 and the only thing, considering that air resistance is insignificant, that is stopping the trolley is the opposing friction. I do not know how to proceed from here.

The teacher also mentioned that it would be useful to also take kinetic and potential energy into consideration. On top of the ramp the trolley will have potential energy, mgh, and as it moves down the ramp, the potential energy is converted into kinetic energy. 0.5 mv^2. But how does that help?!

How would I set this up correctly?
And could someone please explain the concept of the coefficient of friction to me?

Thank you in advance

 

[WalterContrata]

If you understand the problem of the trolley with constant velocity, then you are well started. In that case, the acceleration is zero, and therefore the sum of forces in any direction must be zero. In particular, the sum of forces along the line of motion must be zero.

If the object is accelerating, the vector diagram is the same, but the the forces no longer sum to zero, but to the mass x acceleration. Does that get you started?

About the coefficient of friction, you know that if you slide a block across a table, a force resists the sliding. The force is called friction, and we often assert that it is approximately proportional to the force that the block exerts on the table perpendicular to the table. We call the constant of proportionality "coefficient of friction".

Hope this helps...