A mass m1 = 5.8 kg rests on a frictionless table and connected by a massless string over a massless pulley to another mass m2 = 3.4 kg which hangs freely from the string

Question

A mass m₁ = 5.8 kg rests on a frictionless table and connected by a massless string over a massless pulley to another mass m₂ = 3.4 kg which hangs freely from the string. When released, the hanging mass falls a distance d = 0.77 m.

1)

How much work is done by gravity on the two block system?

3)

What is the final speed of the two blocks?

4)

How much work is done by tension on m₁?

5)

What is the tension in the string as the block falls?

7)

What is the NET work done on m₂?

Answer 1

Hey Anna -- here are some clues that should get you on your way:

1. In this scenario, only m₂ will move downwards, while m₁ will move horizontally.
2. Remember that work only occurs in the direction of a force. This means that gravity is doing work on m₂ but gravity is not doing any work on m₁
3. You can ignore gravity on m₁ throughout this problem
4. Work = Force x distance
5. When the blocks do start moving, they will move at the same speed.
6. This means that the work done by gravity on m₂ will get spread out between the 2 masses.
7. Your answer to part a = KE of mass 1 + KE of mass 2. You can combine those 2 expressions because the speed (v) will be the same.
8. KE = 1/2 m v²
9. You can now find the KE of each block separately with that v that you just found. They should add back up to your answer from a.
10. CHECK: Block 1 should have more kinetic energy, since it's moving the same speed as block 2, but it has more mass.
11. The only force doing work on m1 is tension. It is the only force in the same direction as the block's motion. (Friction would count too, but no friction here)
12. Therefore, whatever KE block 1 possesses HAS to be due to the work from the tension.
13. We also know that block 1 moved 0.77m, so we can go back to work = force x distance to find out what that tension force is.
14. To find the net work on block 2, we need to know the net force. It should be clear that there are 2 forces on block 2: gravity is pulling down, and tension is pulling up. This is the same tension as we just solved for in part 5, since it's all the same rope (and the pulley is massless).
15. Net force = Force of gravity on block 2 - Tension in the string.
16. This net force also acts over a distance of 0.77m, and we again can use the equation Work = Force x distance
17. As a final check, this net work done on block 2 MUST equal block 2's kinetic energy, which we found earlier.

Hope these help!