An object of mass, m1, is placed on a rough table and connected to a string whic

Question

An object of mass, m1, is placed on a rough table and connected to a string which passes under a pulley then over a pulley and then is fastened to a hanging mass, m1. Assuming mi is stationary, how would you measure the coefficient of friction on mi? (That is calculate a formula for mus as a function of m1 and m2) If the mass of m2 is increased until mi accelerates with acceleration a. What is the coefficient of friction, fik in terms of m1( m2, a and gl (Here are a list of hints to help guide you through the problem.) Create free body diagrams for 7^ andm2. Make sure you note that the tension forces on the two objects is the same magnitude. Also remember that the accelerations of the two objects are the same magnitude. Create a formula for the Normal force on m1 From this calculate the Frictional force on Use Newton's second law in the x direction for mus AND use Newton's Second Law in the y direction for m2. Solve for the coefficient of friction muk.

Explanation / Answer

when the two masses are at rest

for m1

force exerted by rope on m1 is the tension force T

frictional force acting = fs = us*m1*g

in equlibrium

T - fs = 0

fs = T .....(1)

for m2

tension force acts in upward direction

gravitational force acts downwards

in equilibrium

T = Fg

T = m2*g..........(2)

from 1 & 2

fs = T = m2*g

us*m1*g = m2*g

us = m2/m1 <<=--------------answer

++++++++++++++

2)

let the masses move with acceleration a

for m1

from newtons second law Fnet = m1*a

net force T - fk = m1*a......(1)

for m2 (moves downward)

net force = m2*a

therefore m2*g - T = m2*a ........(2)

1 + 2

m2*g - fk = a*(m1+m2)

m2*g - uk*m1*a = m1*a + m2*a

m2*g - m1*a - m2*a = uk*m1*a

uk = (m2*g - m1*a - m2*a ) / m1*a

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