A question about elevators

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In summary, the conversation is about a question in a book regarding the motion of an elevator and a ball dropped from its roof. The question asks for the time it takes for the ball to hit the floor and the total distance traveled by the ball relative to the ground. The person asking the question is confused about why the velocity of the elevator is disregarded and is also unsure about how to reach the book's answer for the total distance traveled. The expert advises to include the elevator's velocity if desired and to do all calculations with respect to the ground to find the total distance.
  • #1
Skyblitz
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Hi, there's a question in the book that says:
"An elevator of height 3 m moves upward at 2m/s. A ball is dropped from the roof. a) when does it hit the floor? b) what is the total distance traveled relative to the ground?"

Now, the way I had set it up was that when the ball drops, it falls with an initial velocity of 0m/s and an acceleration of -9.8m/s^2. However, I also took into account the velocity of the elevator moving upwards at 2m/s... I was wondering why we disregard that velocity? (the answer in the book is 0.78s).

Also for part B, I'm not exactly sure how to reach the book's answer. What I did was use the total time, multiplied by the elevator's velocity, so 1.56m. Therefore, once the ball reaches the floor, 0.78 seconds would have passed and thus, it would be 1.56m from the ground. However, the answer is 1.84m, so I'm a little stumped. Any help is appreciated!
 
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  • #2
Originally posted by Skyblitz
Now, the way I had set it up was that when the ball drops, it falls with an initial velocity of 0m/s and an acceleration of -9.8m/s^2. However, I also took into account the velocity of the elevator moving upwards at 2m/s... I was wondering why we disregard that velocity? (the answer in the book is 0.78s).
If the elevator moves uniformly, its motion will not affect any experiments done inside it. (See https://www.physicsforums.com/showthread.php?s=&threadid=10779)

If you want to include the speed of the elevator, be sure to do it completely. The initial speed of the ball with respect to the ground is +2 m/s, same as the elevator.
Also for part B, I'm not exactly sure how to reach the book's answer. What I did was use the total time, multiplied by the elevator's velocity, so 1.56m. Therefore, once the ball reaches the floor, 0.78 seconds would have passed and thus, it would be 1.56m from the ground. However, the answer is 1.84m, so I'm a little stumped. Any help is appreciated!
For part B, do everything with respect to the ground. You know the initial speed and height of the ball. It goes up, then down. You have to find the total distance.
 
  • #3
Thanks a lot for your help!
 

1. How do elevators work?

Elevators use a system of cables, pulleys, and counterweights to move up and down. When the elevator is called to a specific floor, an electric motor turns a pulley that is connected to a cable. This cable is attached to the elevator car and pulls it up or down. The speed and direction are controlled by a computerized system.

2. Are elevators safe?

Yes, elevators are very safe. They are designed with multiple safety features, such as emergency brakes, door sensors, and weight sensors to ensure the safety of passengers. Elevators are also regularly inspected and maintained to ensure they meet safety standards.

3. How much weight can elevators hold?

The weight capacity of an elevator can vary depending on the type and size of the elevator, but most standard elevators can hold anywhere from 2,000 to 5,000 pounds. This weight limit is often displayed inside the elevator and should not be exceeded for safety reasons.

4. Why do elevators sometimes take longer to arrive?

Elevators use a complex algorithm to determine the most efficient route to take, taking into account factors such as the number of people waiting, the weight of the passengers, and the requested floors. This can sometimes cause delays, especially during peak usage times.

5. Can elevators run without electricity?

No, elevators require electricity to operate. Even hydraulic elevators, which use fluid to move the elevator car, require electricity to power the pumps. In the case of a power outage, elevators are equipped with emergency backup systems to lower the elevator to the nearest floor and open the doors for passengers to exit safely.

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