Question

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 mi is stationary, how would you measure the coefficient of friction on mi? (That is calculate a formula for mu s 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, mu k in terms of m1 m2 a and g? Create free body diagrams for m1 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 plusminus . 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 fmu k. Create a template for task 1 and 2 in Excel and bring/email it to class. You can model your template off of the template from Lab 3 (however it will be significantly different since we have a different experimental setup) and the small example on page 4.

Answer 1

Here,

1) let the coefficient of friction is us

Normal reaction for M1 , N1 = m1 * g

Now , for the block m1 to stay stationary

m1 * g * us = m2 * g

us = m2/m1

the coeffcient of friction is m2/m1

Answer 2

The tension due to the block of mass m2 is, T m28 The force on the block of mass m, is due to the friction which is given by s, -u, (mg) Since the block is stationary, This is equal to the tension in the block of mass m2 Thus, therefore, the coefficient of static friction is,