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Answer the following questions An object of mass, mi, is placed on a rough table

ID: 1332017 • Letter: A

Question

Answer the following questions An object of mass, mi, 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, m2. Assuming m1 is stationary, how would you measure the coefficient of friction on m1? ( That is calculate a formula for mu5 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,muk in terms of m 1# m-2, a and g ? Create free body diagrams for m 1 and m2. 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 m i . From this calculate the Frictional force on m1.Use Newton's second law in the x direction for m1 AND use Newton's Second Law in the y direction for m2. Solve for the coefficient of friction muk.

Explanation / Answer

Balancing forces in m2 in vertical,

m2g - T = 0

T = m2g

On m1,

in vertical, N = m1g

friction f = us.m1g

in horizontal, T- f = 0

T = f

m2g = us.m1g

us = m2 / m1

2) now

Balancing forces in m2 in vertical,

m2g - T = m2a

On m2,

in vertical, N = m1g

friction f = us.m1g

in horizontal,   

T- f - m1a

T - uk.m1g = m1a

adding both equation

m2g - uk.m1g = (m1 + m2)a

uk = (m2g - m1a - m2a ) / m1g