How to solve this problem? A block with mass m, is placed on an inclined plane w

Question

How to solve this problem?

A block with mass m, is placed on an inclined plane with slope angle and is connected to a second hanging block with mass m2 by a cord passing over a small, frictionless pulley (see Figure). The coefficient of static friction is and the coefficient of kinetic friction is k. a) Find the mass m2 for which block mi moves up the plane at constant speed once it is set in motion. once it is set in motion. released from rest? b) Find the mass m2 for which block mi moves down the plane at constant speed c) For what range of values of m2 will the blocks remain at rest if they are

Explanation / Answer

a)

when block m1 moves upward:

forces on m1 are:

friction: Ffr = m1*g*cos(a)*uk

gravity: Fg = m1*g*sin(a)

cord tension: Ft

Ft = Fg + Ffr

Ft = m1*g * [sin(a) + uk*cos(a)]

also Ft = m2*g

m2 = m1*[sin(a) + uk*cos(a)]

b)

when block m1 moves downward:

Ft + Ffr = Fg

Ft = m1*g * [sin(a) - uk*cos(a)]

also Ft = m2*g

m2 = m1 * [sin(a) - uk*cos(a)]

c)

This time using coefficient of static friction (us)

The minimum mass m2 that allows system to be stationary

m2(min) = m1*[ sin(a) - us*cos(a)]

m2(max) = m1*[ sin(a) + us*cos(a)]

The range is m1*[ sin(a) - us*cos(a)] to m1*[ sin(a) + us*cos(a)]

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