Suppose the elevator now accelerates down-
ward at a constant rate of 0.13 g.
What is the ratio of the new scale reading
to the value W of the scale reading when the
elevator is at rest?
Wdown= mg-ma
ratio= 1-a/g
sdf
To find the ratio of the new scale reading to the value W of the scale reading when the elevator is at rest, we need to consider the acceleration due to gravity and the additional acceleration caused by the downward acceleration of the elevator.
Here are the steps to find the ratio:
1. Identify the acceleration due to gravity: In this case, it is usually given as 9.8 m/s^2, which is equivalent to 1g. Since the elevator is accelerating downward, we need to consider its effect:
- The elevator's downward acceleration is given as 0.13g, where g is the acceleration due to gravity.
- Multiplying 0.13g by the acceleration due to gravity (9.8 m/s^2) will give us the actual acceleration of the elevator in m/s^2.
2. Calculate the scale reading at rest: The scale reading when the elevator is at rest is equal to the weight of the person inside the elevator.
- The weight can be calculated by multiplying the mass of the person by the acceleration due to gravity.
- Assuming the mass of the person is known, multiply it by 9.8 m/s^2 to get the scale reading at rest (W).
3. Calculate the scale reading with the downward acceleration:
- Add the downward acceleration due to the elevator (from step 1) to the acceleration due to gravity.
- Multiply the total acceleration by the mass of the person to get the new scale reading.
4. Calculate the ratio:
- Divide the new scale reading (from step 3) by the scale reading at rest (W) calculated in step 2.
By following these steps, you can find the ratio of the new scale reading to the value W of the scale reading when the elevator is at rest.