Question

Two identical solid disks of unknown mass are moving on horizontal surfaces. The center of mass of each disk has the same linear speed of 8.5 m/s. One of the disks is rolling without slipping, and the other is sliding along a frictionless surface without rolling. Each disk then encounters an inclined plane 15° above the horizontal. One continues to roll up the incline without slipping while the other continues to slide up, again without friction. Eventually, they come to a momentary halt due to gravity slowing them down.

Determine the maximum distance along the incline each disk moves before coming to a stop.

Answer 1

for the sliding disk 1

initial kinetic energy K1i = (1/2)*m*v^2

work done by gravity Wg = -m*g*L*sintheta

final kinetic energy K1f = 0

work done = change in KE

-m*g*L*sintheta = - (1/2)*m*v^2

L = v^2/(2*g**sintheta)

L = 8.5^2/(2*9.8*sin15) = 14.24 m

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for rolling disk 2

initial kientic energy K2i = (1/2)*m*v^2 + (1/2)*I*w^2

w = angular speed = v/r

I = moment of inertia = (1/2)*m*r^2

K2i = (3/4)*m*v^2

work done by gravity Wg = -m*g*L*sintheta

final kinetic energy K2f = 0

work done = change in KE

-m*g*L*sintheta = - (3/4)*m*v^2

L = 3v^2/(4*g**sintheta)

L = 3*8.5^2/(4*9.8*sin15) = 21.36 m