Question on Forces and Friction

The better question is, how could you put slabs of stone to work as you do, but not give them a name? I offer the names Bedrock and Rocky. Other names can apply.

Draw yourself a picture of this before you start.

1) For the block on the ramp, the normal force to the ramp is cos(30) x m x g. Cos(30) = .866 and g = 9.2 m/s^2. The force of friction is the friction coefficient f times the normal force.

The in-line force the block exerts is sin(30) x m x g = .5 mg

For the block hanging, the force is just the force of gravity mg. Set these equal to each other.

mg = f (.866) mg + .5mg
1 = .866f + .5
f = .5 / .866 = .577
Note that f could be higher than this. This is a minimum.

2) Without the friction term above, the net force on the two block system is 0.5 mg. The total mass is 2m so the acceleration is F/m = 0.5mg / 2m = 0.25 g = 2.3 m/s^2

Distance traveled = 1/2 a t^2 = 0.5m. Solve for t, t=0.66 seconds
Velocity = a t = 2.3 x 0.66 = 1.52 m/s