Interesting deal with friction and energy

[DaMastaofFisix]

Hey everyone, I have a free response question concerning some rather simple mechanics presented in a ratheruh...interesting way. We have a block of mass M, that slides don a hill at an angle of theita. the block slides down the hill from rest at s=0 to the final position/distance s. Here's the catch. The coefficient of friction is u=as, where a is a constant and s is the distance down the hill. So its obvious that this is an incresingly rough incline.

a) Show all the forces acting on the block, in terms of only what's given (and g)
b) Draw a frictional force versus distance graph
c) Fins the area under the graph to deteminr the work done on the block
d) Find out how far the block slides down the hill

This is a doosey. I understand the setup for all of the steps,but the problem comes in verifying my algebra and making sure I am using the right setup. all answers must be expressed in terms of the quantities given. I got some answers, most importantly that the distance is tan(theita)/a. Will someone help me OUT?!

 

[DaMastaofFisix]

If y'all need to see some more work, let me know, I'll upload everything I have.

 

[daniel_i_l]

For b) just find the normal force and write a linear equation with the friction, distance, and normal (f(s)=N*a*s)
c) simple geometry
d) check when the friction is greater than the componant of gravity that's pulling the block down the hill.

 

[Doc Al]

I got some answers, most importantly that the distance is tan(theita)/a.

It looks like you solved for the point where the friction force equals the component of gravity down the slope; instead, find the point where the change in gravitational PE equals the work done by the friction force.

 

[DaMastaofFisix]

Thanks guys, helped a whole bunch. I new I was on the right track, but I got stuck at the crossroads. Thanks a bunch. Next post coming up will be thw work that I've done.