Elevator Problem
Answers

1. Elevator At Rest
   1. What does the scale say?
      1. scale pushes with a force of 500 Newtons (to balance the Earth's pull)
      2. scale says 500 Newtons (equal to the scale's push)
   2. What does the apple do?

   
   
   

2. Elevator Accelerates Up
   3. What does the scale read? To complete the force diagram you need to an upward force on you due to the scale. This force turns out to be 600 Newtons - see below.
      1. the scale pushes with a force of 600 Newtons, since when the scale's force is combined with the Earth's force (weight = 500 Newtons) there has to be a 100 Newton force (upward) left over - the net force.
      2. 600 Newtons (same as part a)
      3. 600 Newtons (same as the force the scale exerts)
   4. What does the apple do?

   
   
   

3. Elevator at Constant Velocity
   5. What does the scale read? To complete the force diagram, you need to add an upward force on you due to the scale. This force turns out to be 500 Newtons - see below.
      1. The scale's force on you is 500 Newtons. (see below)
      2. Your acceleration is 0 m/s² (since your velocity is constant)
      3. 0 m/s² (same as part b)
      4. The net force must be 0 Newtons (if the acceleration is 0 m/s²).
      5. 0 Newtons (same as part d)
      6. The scale's force must be 500 Newtons since it must exactly balance your weight (500 Newtons) so that the net force is 0 Newtons.
      7. The scale reads 500 N (same as the scale's force).
   6. What does the apple do if you let go? The apple would be in free fall, so its acceleration relative to the Earth would be 9.8 m/s². Its acceleration relative to you would be the same (since your acceleration is 0 m/s²) so the apple would fall exactly as it would if the elevator were at rest.

   
   
   

4. Elevator Accelerates Downward (While Going Up)
   7. What does the scale read? To complete the diagram, add an upward force on you due to the scale. This force turns out to be 400 Newtons - see below.
      1. Your weight is 500 Newtons (given in the problem)
      2. The scale's force is 400 Newtons (see below)
      3. Your mass is 50 kilograms (given in the problem)
      4. Your acceleration is 2 m/s²
      5. The net force is 100 Newtons (= (50 kg)(2 m/s²))
      6. 100 N (same as part e)
      7. 100 N (same as part e)
      8. The scale's force is 400 Newtons, since it must combine with your weight (500 Newtons) to leave a net downward force of 100 Newtons.
      9. The scale reads 400 Newtons (same as scale's force)
   8. What does the apple do if you drop it? Relative to the Earth, the apple accelerates toward the Earth at about 10 m/s², but you are accelerating toward the Earth, too, at 2 m/s². The apple's acceleration relative to you is 10 m/s² - 2 m/s² = 8 m/s² - the apple seems to fall slower than "normal" free fall.

   
   
   

5. The Elevator Speeds Up - While Going Down - This is exactly the same as Part D! The direction the elevator moves doesn't matter - only the direction the elevator accelerates. Since the elevator is accelerating downward in both cases, the situation inside the elevator is identical!
   
   
6. The Elevator Moves Down With Constant Speed - This is exactly the same as Part C! The direction that the elevator moves doesn't matter - only the elevator's acceleration. In both cases, the elevator's acceleration is 0 m/s², so the situation inside the elevator is the same in both cases.
   
   
7. Oh! No!
   13. What does the scale read?
       1. 500 Newtons
       2. 0 Newtons
       3. 10 m/s/s (= g)
       4. 50 kg (your mass)
       5. 10 m/s/s (= g)
       6. 500 Newtons
       7. 500 Newtons
       8. 500 Newtons
       9. 0 Newtons
       10. 0 Newtons
   14. If you let go of the apple, what does it do? Your acceleration and the apple's acceleration are equal (10 m/s² downward, so you both fall at the same rate. Relative to you, the apple stays right where you let go of it - it appears to float. In other words, the apple appears to be weightless, just as it would aboard the space shuttle orbiting the earth!
   15. What can you do to be weightless? You could jump up in the air, or jump off a chair. While you are falling, you are weightless! If you jump off a chair holding an apple, and let go of the apple, the apple will appear to float right where you left it (relative to you) - it is weightless!