Consider the system of masses, strings, and pulleys connected as shown. The strings are massless and inextensible, and the pulleys are massless and frictionless. There is a uniform gravitational field g. Note that only the lower pulley is free to move up and down. Treat the first string of length l1 as beginning at the upper edge of m1, going around the upper pulley, and ending at the center of the lower pulley. The second string of length l2 is attached to the floor, goes around the lower pulley, and ends at the upper edge of m2
a. Write down expressions for the lengths l1 and l2 of the strings in terms of x1, x2, p1, p2, and the pulley radius R (consider the hook on the floor to be part of string l2). (1 pt)
b. Sketch the free-body diagram for each mass, and write down the force equations from Newton's second law. Use a1 and a2 for the accelerations of masses m1 and m2, respectively. (1 pt)
c. Using the result from part (a), find the relationship between a1 and a2. In other words, a1=ka2, where k is a numerical constant. (1 pt)
d. Write down the relationship between the tensions in the strings T1 and T2. In other words, T1=k2T2, where k2 is a numerical constant. (1 pt)
e. Solve for a1 and T2 in terms of m1, m2, and g. If you are unable to work parts (c) and (d) correctly, use a1= -a2 and T1=1/3 T2. (Note: these are not the correct relations.) (1 pt)
f. What is a2 in the case of m1=m2 ?
What is the condition for zero acceleration of the masses? (1 pt)