Classical Mechanics - Blocks

Basic problem type: Block of mass m is angled at theta, find the coefficient mu for the static friction that is keeping the block in place.

Method: look at the forces on and perpendicular to the ramp. First, resolve F_g, the force due to gravity.

When theta=0, the ramp is flat, and there is no force in ramp direction. F_g = perpendicular (F_g|| = 0).

When theta= pi/2, gravity force is all parallel, F_g_perpendicular = 0. Block falls down.

For block to not accelerate perpendicularly, the normal force N must be equal to mgcos(theta)

Set equations for friction and force of gravity parallel to each other to solve for mu.

Equations for blocks on ramps:

F_g||= mgsin(theta)

F_g_perp = mgcos(theta)

N = mgcos(theta) for perpendicular balance

F_fric = mu*mgcos(theta) to balance component of gravity parallel

F_g||=mgsin(theta)

mu*mgcos(theta)=mgsin(theta) --> mu=tan(theta)

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