I just need help with part c. I know stopping takes longer but we have to explain why.
A student stands on a bathroom scale in an elevator at rest on the 64th floor of a building. The scale reads 849 N.
(a) As the elevator moves up, the scale reading increases to 912 N. Find the acceleration of the elevator.
0.73 m/s^2
(b) As the elevator approaches the 74th floor, the scale reading drops to 782 N. What is the acceleration of the elevator?
-0.77 m/s^2
(c) Using your results from parts a and b, select which change in velocity, starting or stopping, takes the longer time.
To determine which change in velocity (starting or stopping) takes a longer time, we can look at the acceleration values from parts (a) and (b) and consider the physics concepts involved.
In part (a), the acceleration of the elevator while moving up is determined to be 0.73 m/s^2. This indicates that the elevator is accelerating in the upward direction.
In part (b), the acceleration of the elevator while approaching the 74th floor is determined to be -0.77 m/s^2. The negative sign indicates that the elevator is decelerating or slowing down.
Based on these acceleration values, we can conclude that the acceleration in part (b) is higher in magnitude than in part (a) since -0.77 m/s^2 is greater than 0.73 m/s^2. This means that stopping the elevator (deceleration) takes longer than starting (acceleration) because a higher magnitude of acceleration is required to slow down the elevator compared to starting it.
So, to answer part (c), stopping the elevator takes the longer time compared to starting it.
To determine which change in velocity takes longer, we need to compare the time it takes for the elevator to accelerate from rest to its final velocity, versus the time it takes for the elevator to decelerate and come to a stop.
In part (a), we found that the elevator had an acceleration of 0.73 m/s^2 while moving up. This means that the elevator is accelerating in the same direction as its initial motion, which is upwards.
In part (b), we found that the elevator had an acceleration of -0.77 m/s^2 while moving up towards the 74th floor. This means that the elevator is decelerating, or accelerating in the opposite direction to its initial motion, which is downwards.
Since the acceleration in part (b) is negative and opposite to the direction of the initial motion, we can conclude that it represents the deceleration or the time taken to stop the elevator.
Therefore, the change in velocity required to stop the elevator takes longer than the change in velocity required to start the elevator.