2 m 05 m 30 SolutionThe inclination of the plane creates rol

Solution

The inclination of the plane creates rolling of the disk, and forces acting on the slider is given by,

m1g cos theta + m2g cos theta, where theta is the resultant inclined force due to slider and rod masses.

The rolling of the disk creates an angular sweep of theta 45 degree, inducing a linear kinectic energy while theta = 0.

The kinectic energy is given by,

1/2 * m1 * v^2 = F x distance ------- eqn 1

Distance the silder travels = cos 45 * 2 = 1.414 m

F = m1g cos theta + m2g cos theta, where theta = 60deg

F = 5 * 9.81 * cos 60 + 16 * 9.81 * cos 60 = 78.48 + 25.525 = 103.005 N

Replacing the values in eqn 1,

1/2 * 5 * v^2 = 103.005 * 1.414

velocity = 7.6327 m / s