Question

2. Atwood's Table with Two Hanging Masses

You have table of width L, masses m1, m2, and m3, two frictionless pulleys, and ideal string. Placing m2 on the table, you attach a bit of string to mass m1 the left pulley, to the left side of m2. Similarly, you hang mass m3 from the right side of m2 using the pulley on the right side of the table. The coefficient of friction of the table is mu. The acceleration of gravity is g. Derived expressions are in some or all of the m1, m2, m3, mu, L, and g.

1) Draw a physical diagram of the system, and free body diagrams of each block, showing only relevant forces, fully labeled.

2) Write the Newton's second law equation for each block. Three equations. Identify the three unknowns.

3) Derive, using forces and Newton's second law, an expression for the acceleration of the masses.

4) Derive, using the energy method, an expression for the acceleration of the masses.

5) Derive an expression for the value of mu that makes the value of the acceleration zero.

6) Derive an expression for the time it takes mass m2 to move the width of the table starting from rest.

7) Derive expressions for the tensions T1 and T2 in the left and right strings, respectively.

8) Calculate the ratio T1/T2.

Answer 1

table of width L,

masses m1, m2,

and m3,