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 14 m/s. It then travels on a horizontal surface without friction, around a circular loop without falling off, 011 another horizontal surface without friction, up a ramp with a length of 24 meters, with a coefficient of kinetic friction of 0.61 which is inclined at 48 degrees. It then ends up 011 a horizontal frictionless surface moving at a speed of 20 m/s. What is the radius of the quarter circular ramp, in meters, the mass started?

Explanation / Answer

Apply law of conservation of energy

m*g*R1 + 0.5*m*vi^2 = 0.5*m*5*R2*g = [m*g*sin(theta)+ mu_k*m*g*cos(48)]*l = 0.5*m*vf^2

m cancels

9.81*R1 + 0.5*14^2 = 0.5*20*20

R1 = 10.4 m

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