Question

High-speed elevators function under two limitations: (1) the maximum magnitude of vertical acceleration that a typical human body can experience without discomfort is about 1.2 m/s2, and (2) the typical maximum speed attainable is about 9.5 m/s . You board an elevator on a skyscraper's ground floor and are transported 200 m above the ground level in three steps: acceleration of magnitude 1.2 m/s2 from rest to 9.5 m/s , followed by constant upward velocity of 9.5 m/s , then deceleration of magnitude 1.2 m/s2 from 9.5 m/s to rest. Determine the elapsed time for each of these 3 stages, and Determine the change in the magnitude of the normal force, expressed as a % of your normal weight during each stage.

Answer 1

The elapsed time for each stage can be found using the kinematic equations. The change in the magnitude of the normal force can be calculated by considering the forces acting on the body. The first and third stages result in a 11.7% decrease in the normal force.

Step-by-step explanation:

To determine the elapsed time for each stage, we can use the kinematic equations. For the first stage, we can use the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time. Solving for t, we get t = (vf - vi) / a. Plugging in the given values, we get t = (9.5 m/s - 0 m/s) / 1.2 m/s^2 = 7.92 s. For the second stage, we know that the elevator is moving at a constant velocity of 9.5 m/s, so the time taken will be 200 m / 9.5 m/s = 21.05 s. For the third stage, we can use the same equation as in the first stage, but with different initial and final velocities. Plugging in the given values, we get t = (0 m/s - 9.5 m/s) / -1.2 m/s^2 = 7.92 s.

To determine the change in the magnitude of the normal force during each stage, we need to consider the forces acting on the body. At rest, the normal force is equal to the weight of the body, which is mg. During the first stage, the normal force will be less than mg due to the acceleration. We can calculate this as a percentage of the normal weight by dividing the difference in normal force by mg and multiplying by 100%. The difference in normal force is given by F = ma, where F is the force, m is the mass, and a is the acceleration. Plugging in the given values, we get F = 60 kg * 1.2 m/s^2 = 72 N. The difference in normal force is therefore 72 N. Dividing by mg and multiplying by 100%, we get a change of (72 N / (60 kg * 9.8 m/s^2)) * 100% = 11.7%. During the second stage, the elevator is moving at a constant velocity, so there is no change in the normal force. During the third stage, the normal force will be greater than mg due to the deceleration. Using the same calculation as in the first stage, we find that the change in the normal force is -11.7%.

Learn more about High-speed elevators