A mass starts at the top of a quarter circular ramp with some radius at a speed

Question

A mass starts at the top of a quarter circular ramp with some radius at a speed of 8 m/s. It then travels on a horizontal surface without friction, around a circular loop without falling off, on another horizontal surface without friction, up a ramp with a length of 22 meters, with a coefficient of kinetic friction of 0.62 which is inclined at 39 degrees. It then ends up on a horizontal frictionless surface moving at a speed of 24 m/s. What is the radius of the quarter circular ramp, in meters, the mass started?

Explanation / Answer

Use equation,

Initial ME = Final ME

PEi+KEi + Ei = PEf+KEf + Ef

Ef= frictional energy

mgR +1/2mvi^2 + 0 = mg22sin39+1/2mvf^2+uk*mgcos39

R=radius of circular ramp

m cancels

gR +1/2vi^2 + 0 = g22sin43+1/2vf^2+uk*gcos39

Plugging values,

9.8*v +0.5*8^2 + 0 = 9.8*22sin39+0.5*24^2+0.62*22cos39     => R= 41.05m

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