Elevator falling and bouncing back from a spring

Thread starter jolly_math
Start date Oct 24, 2022
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Elevator Falling Spring

In summary, the concept of an elevator falling and bouncing back from a spring involves a hypothetical scenario where an elevator is suspended by a spring and experiences a downward force, causing it to fall and bounce back. This is caused by the principles of gravity and elasticity, but it is not possible in real life due to safety mechanisms and the limitations of the spring's force. The height of the elevator affects the speed and magnitude of its fall and bounce back, and while there are no real-life applications for this concept, understanding it can help improve safety mechanisms for elevators and other devices.

Oct 24, 2022

jolly_math

Homework Statement: The cable of a 4000-lb elevator snaps when the elevator is at rest at the first floor so that the bottom is a distance d = 12.0 ft above a cushioning spring whose force constant is k = 10,000 lb/ft. A safety device clamps the guide rails, removing 1000 ft-lb of mechanical energy for each 1.00 ft that the elevator moves.
(a) Find the speed of the elevator just before it hits the spring.
(b) Find the distance that the spring is compressed.
(c) Find the distance that the elevator will bounce back up the shaft.
(d) Calculate approximately the total distance that the elevator will move before coming to rest. Why is the answer not exact?

Relevant Equations: U(x) (gravity) = mgh
U(x) (spring) = (1/2)kx^2
KE = (1/2)mv^2

I don't understand the difference between part c and d. After compressing the spring, the elevator bounds back and moves before coming to rest in both cases. What is the difference? Thank you.

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Oct 24, 2022

BvU

Science Advisor

Homework Helper

Hi,

Well, after c, the thing is still up in the air and will start to go down again, etc, until all energy has been dissipated.

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1. How does a spring prevent an elevator from falling?

When an elevator falls, the spring inside it compresses and absorbs the potential energy of the falling elevator. This compression creates an upward force that counteracts the downward force of gravity, preventing the elevator from falling further.

2. How does the spring make the elevator bounce back?

After the spring has absorbed the potential energy of the falling elevator, it releases that energy as the elevator reaches the bottom of its fall. This causes the spring to expand and push the elevator back up, creating a bouncing motion.

3. Can a spring break and cause the elevator to fall?

While it is possible for a spring to break, it is highly unlikely that it would cause an elevator to fall. Elevator springs are designed with high safety factors and are regularly inspected and replaced to ensure their reliability.

4. Is the spring the only mechanism that prevents an elevator from falling?

No, there are multiple safety mechanisms in place to prevent an elevator from falling. These include the elevator's braking system, counterweights, and emergency brakes. The spring is just one component of the overall safety system.

5. Can an elevator bounce back too high and cause damage?

No, elevators are designed with safety features that prevent them from bouncing back too high. These features include shock absorbers and limit switches that stop the elevator at a safe height. In rare cases where these safety features fail, the elevator will still not bounce back high enough to cause significant damage.