Suppose you hang an object of weight W by a string from a hanging spring scale, such as the kind used in some grocery stores. You then hang the scale with the object from the ceiling of an elevator. When the elevator is standing still, the scale will read the actual weight of the object, W. What will the scale read in each of the following situations: 1) when the elevator is accelerating upward; 2) when the elevator is accelerating downward; 3) when the elevator is falling freely?

Question

Suppose you hang an object of weight W by a string from a hanging spring scale, such as the kind used in some grocery stores. You then hang the scale with the object from the ceiling of an elevator. When the elevator is standing still, the scale will read the actual weight of the object, W. What will the scale read in each of the following situations: 1) when the elevator is accelerating upward; 2) when the elevator is accelerating downward; 3) when the elevator is falling freely?

Answer 1

The reading R will be

R>W
R<W
R=0

Answer 2

To determine what the scale will read in each situation, we need to consider the forces acting on the object when it is in different states of motion.

1) When the elevator is accelerating upward:
- The object experiences two forces: its weight W acting downward (due to gravity) and the upward force of the scale.
- The scale will read a value greater than W.
- This is because the scale needs to exert a greater upward force to counteract the object's weight and the additional force due to the elevator's acceleration.

2) When the elevator is accelerating downward:
- Similar to the previous case, the object experiences its weight W acting downward, but now the acceleration of the elevator is in the same direction.
- The scale will read a value less than W.
- This is because the scale needs to exert a smaller upward force to counteract the combined effect of the object's weight and the downward acceleration of the elevator.

3) When the elevator is falling freely:
- In this case, the elevator is in free fall, meaning that both the elevator and the object are accelerating downward at the same rate, due to gravity.
- The object experiences its weight W acting downward, but there is no scale to exert any additional upward force.
- The scale will read zero.
- This is because there is no external force opposing the object's weight, so there is no force registered by the scale.

In summary:
1) Scale reads a value greater than W when the elevator is accelerating upward.
2) Scale reads a value less than W when the elevator is accelerating downward.
3) Scale reads zero when the elevator is falling freely.