Try this problem:
A 30 kg block sits on a ramp that is 2 meters long at a
45 degree angle. It slides down the ramp with NO friction.
Then it slides along the rough floor
and stops after 10 meters.
What is the coefficient of friction
between the block and the floor?
2 parts: ramp and floor
Mass of block=30 kg
Weight of block=W=mg=30*9.8=294 N
Parallel force down ramp=Wsin =294*sin45=207.89 N
Acceleration= Fnet=Fparallel=207.89=mA, 207.89=30*A, A= 207.89/30=6.93 m/s2
Final velocity= sqrt (2*A*D)= sqrt (2*6.93*2)=5,26 m/s
Initial velocity= 5.26 m/s
Final velocity= 0
Weight of block= 294 N
Normal force= 294 N
Distance= 10 m
Deacceleration= Vi2/2D = 5.262/(2*10) =-1.386 m/s2
Force friction=Fnet=mA=30*1.389=41.6 N=uFn =u (294)
Coefficient of friction= 41.6/294=.14
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