A solid cylinder of mass 0.20kg and radius 1.00cm is released fromrest at the to

Question

A solid cylinder of mass 0.20kg and radius 1.00cm is released fromrest at the top of a 45 degree incline whose height is 1.00m. Itrolls without slipping to the bottom of the incline and continuesto roll without slipping on the horizontal surface with the speedit reached at the bottom of the incline. The cylinder thenencounters another incline, this one making an angle of 30 degreeswith the horizontal. It moves up the second incline withoutslipping.
Calculate the center of mass speed of the cylinder when itreaches the bottom of the first incline.
Find the distance along the second incline that the cylinderwill travel before it rolls back down.
Once it rolls back down to the horizontal surface, what willbe its speed?
If it continues to roll back to the first incline with thisspeed and then rolls back up on the first incline, all withoutslipping, what distance will it travel along the firstincline?
How long will it take the cylinder to reach the bottom of thefirst incline starting from when it is at its highest distance upthe incline?
Calculate the center of mass speed of the cylinder when itreaches the bottom of the first incline.
Find the distance along the second incline that the cylinderwill travel before it rolls back down.
Once it rolls back down to the horizontal surface, what willbe its speed?
If it continues to roll back to the first incline with thisspeed and then rolls back up on the first incline, all withoutslipping, what distance will it travel along the firstincline?
How long will it take the cylinder to reach the bottom of thefirst incline starting from when it is at its highest distance upthe incline?

Explanation / Answer

Calculate the center of mass speed v of the cylinder when itreaches the bottom of the first incline.
mgh = mv2/2 + I2/2 = mv2/2 +(mr2/2)(v/r)2/2 = 3mv2/4
v = (4gh/3) = 3.61 m/s

Find the distance d along the second incline that the cylinderwill travel before it rolls back down.
mv2/2 + I2/2 = mgdsin'
mgh = mgdsin'
d = h/sin' = 2.00 m

Once it rolls back down to the horizontal surface, what willbe its speed?
v = 3.61 m/s (because energy conservation)

If it continues to roll back to the first incline with thisspeed and then rolls back up on the first incline, all withoutslipping, what distance will it travel along the firstincline? d' = h/sin = 1.41 m

How long will it take the cylinder to reach the bottom of thefirst incline starting from when it is at its highest distance upthe incline?

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