Question

Figure shows a block of mass m resting on a 20? slope. The block has coefficients of friction 0.82 and 0.49 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg.

What is the minimum mass m that will stick and not slip?

If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have?

Answer 1

On a 20 deg slope
The force which is parallel will cause acceleration down the incline
F p = mass * 9.8 * sin theta = m * 9.8 * sin 20

Friction force will be caused by the force perpendicular to it
= mass * 9.8 * cos theta
= F p = m * 9.8 * cos 20

Friction force :
= us * m * 9.8 * cos 20

Summation of forces down
= m * 9.8 * sin 20 + us * m * 9.8 * cos 20
= m * 9.8 * sin 20 + 0.82 * m * 9.8 * cos 20
= m * 9.8 * (sin 20 + 0.82 *cos 20 )
= m * 9.8 * (sin 20 + 0.82 *cos 20 )

The force caused by the 2 kg = 2 * 9.8 = 19.6 N pulling the block up the slope.

(a)
The block will stick and not slip, if the sum of the down forces < 19.6 N

m * 9.8 * (sin 20 + 0.84 *cos 20 ) < 19.6
m < 19.6 / [9.8 * (sin 20 + 0.82 *cos 20 )]
m < 1.8 Kg


(b)
19.6

Answer 2

A block of mass m resting on a 20