How do i find the acceleration of a cylinder's center of mass while it is on a incline ramp? It starts initially at the top of the ramp and slides down the ramp

1 Answer
Steve J.
Feb 1, 2018

The acceleration is #g*(sintheta - mu_k*costheta)#.

Explanation:

Let the angle between the incline and horizontal be #theta#. Let the coefficient of kinetic friction be #mu_k#. Let the mass of the cylinder be m.

The component of the cylinder's weight that points down the incline, #w_"ds"#, would be

#w_"ds" = m*g*sintheta #

The force of friction #F_f#, would be

#F_f = mu_k*N = mu_k*m*g*costheta#

Therefore the net force acting on the cylinder, #F_"net"#, would be the difference between the affect of the weight (wanting to slide down the incline) and the affect of friction (wanting to inhibit sliding).

#F_"net" = w_"ds" - F_f#

#F_"net" = m*g*sintheta - mu_k*m*g*costheta#

#F_"net" = m*g*(sintheta - mu_k*costheta)#

From Newton's 2nd Law then, the acceleration is

#a = (m*g*(sintheta - mu_k*costheta))/m = g*(sintheta - mu_k*costheta)#

I hope this helps,
Steve

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