A block with mass m1 is placed on an inclined plane with slope angle and is conn

Question

A block with mass m1 is placed on an inclined plane with slope angle and is connected to a second hanging block that has mass m2 by a cord passing over a small, frictionless pulley. The coefficient of static friction is s and the coefficient of kinetic friction is k. (Figure 1) a)Find the mass m2 for which block m1 moves up the plane at constant speed once it has been set in motion. Express your answer in terms of m1, m2, , k, and s. b)Find the mass m2 for which block m1 moves down the plane at constant speed once it has been set in motion. Express your answer in terms of m1, m2, , k, and s. c)Find the smallest value of m2 when the blocks will remain at rest if they are released from rest. Express your answer in terms of m1, m2, , k, and s.

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 = 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) based on results in the previous two sections:
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)]

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