Question

In the figure below, the pulleys and the cord are light, all surfaces are frictionless, and the cord does not stretch.
(a) How does the acceleration of block 1 compare with the acceleration of block 2?

(b) The mass of block 2 is 1.30 kg. Find its acceleration as it depends on the mass m1 of block 1.

(c) What does the result of part (b) predict if m1 is very much less than 1.30 kg?

(d) What does the result of part (b) predict if m1 approaches infinity?
(e) In this last case, what is the tension in the cord?

Picture: http://www.webassign.net/serpse8/5-p-066.gif

Answer 1

Block 2 experiences gravitational acceleration, block 1 does not.

Answer 2

This is an interesting problem. As m2 goes down, it accelerates and tugs on m1, which accelerates also. The tension, T will be the same throughout the rope, which means 1 T pulling on m1 and 2 T pulling on m2. Whatever the acceleration of m2, the acceleration of m1 is twice that, because length L of rope motion at m1 yields L/2 of motion of m2, supported by two strands of rope.

For m1: T = m1 a

for m2: 2T - m2 a/2 = m2 g

We have two equations and two unknowns, T and a. Solvable.

If m1 is very small, T goes to zero and m2 falls freely.

If m1 very large, m2 is just suspended by 2 T = m2 g