# Gravitational elevator (physics Torque question)

• sweetiev
In summary, the conversation discusses designing an emergency escape device for a high rise building that uses a gravitational powered elevator. The design involves a turntable on the roof with a cable attached to a wire cage that can hold 5 people. The design is then tested by calculating the acceleration of the fully loaded elevator, with the radius and mass of the turntable and vertical pulley provided. The conversation also mentions the use of equations such as the moment of inertia and Newton's second law to solve for the acceleration.
sweetiev

## Homework Statement

After watching a news story about a fire in a high rise apartment building, you and your friend decide to design an emergency escape device from the top of a building. To avoid engine failure, your friend suggests a gravitational powered elevator. The design has a large, heavy turntable (a horizontal disk that is free to rotate about its center) on the roof with a cable wound around its edge. The free end of the cable goes horizontally to the edge of the building roof, passes over a heavy vertical pulley, and then hangs straight down. A strong wire cage which can hold 5 people is then attached to the hanging end of the cable. When people enter the cage and release it, the cable unrolls from the turntable lowering the people safely to the ground. To see if this design is feasible you decide to calculate the acceleration of the fully loaded elevator to make sure it is much less than g. Your friend's design has the radius of the turntable disk as 1.5 m and its mass is twice that of the fully loaded elevator. The disk which serves as the vertical pulley has 1/4 the radius of the turntable and 1/16 its mass. In your trusty Physics book you find that the moment of inertia of a disk is 1/2 that of a ring.

I think..

Ir=1/2MR^2
Tnet=I(alpha)
Fg-Fr=ma
ar=(Fg-Fr)/Msp

## The Attempt at a Solution

I honestly have no idea. Can someone please get me started on it?

Like I have

T1(1.5m)=I(alpha)
T1= [(1/2*m*R^2)(alpha)]/1.5m b/c torque= T1(R)=I*alpha

oh and

there will be T1 and T2,

so Sum of torque = T2(Rp) - T1(Rp) = I*alpha

and... I don't know, I don't understand :(

Last edited:
You need three separate free body diagrams, for the disk, for the pulley and for the hanging cage with people. Use them to write three Newton's 2nd Law equations. Note that you have three unknowns, two tensions and an acceleration. Solve for the acceleration.

I would first commend your curiosity and critical thinking in trying to determine the feasibility of your friend's design. It is always important to consider the physics and mechanics behind any proposed solution.

To get started on this problem, we can first define some variables:
- M = mass of fully loaded elevator
- m = mass of turntable
- R = radius of turntable
- Rp = radius of pulley
- I = moment of inertia of a disk (1/2 MR^2)
- alpha = angular acceleration
- T1 = torque applied by the cable on the turntable
- T2 = torque applied by the cable on the pulley
- Fg = weight of elevator and passengers
- Fr = frictional force between the cable and the turntable
- a = linear acceleration of the elevator

Using the equations you have listed, we can set up the following equations:
1. Torque balance: T2(Rp) - T1(Rp) = I*alpha
2. Net force: Fg - Fr = Ma
3. Angular acceleration and linear acceleration are related by: alpha = a/R

We can also use the given information to determine the values of T1 and T2:
- T1 = (m+M)g, where g is the acceleration due to gravity
- T2 = Mg

Substituting these values into our equations, we get:
1. (Mg)(Rp) - [(m+M)g](Rp) = (1/2 MR^2)(a/R)
2. (Mg) - [(m+M)g] = (M+m)a

Simplifying and rearranging, we get:
1. a = (g/2)(M/m+M)
2. a = (g/2)(M/m+M)

Since we want the acceleration to be much less than g, we can set an upper limit for a, say 0.1g. This means that (M/m+M) should be less than 0.2. This is a feasible value, as the mass of the turntable is twice that of the fully loaded elevator, so (M/m+M) would be around 0.33.

Therefore, based on these calculations, your friend's design seems feasible and could potentially be a viable solution for an emergency escape device. However, it is important to also consider other factors

## 1. What is a gravitational elevator?

A gravitational elevator, also known as a space elevator, is a theoretical structure that would allow objects to travel from the surface of a planet (such as Earth) into space without the use of rockets. It would use the planet's own gravity and the centrifugal force of its rotation to lift objects up a long cable or tower.

## 2. How does a gravitational elevator work?

A gravitational elevator works by balancing the forces of gravity and centrifugal force. The base of the elevator would be anchored to the surface of the planet, while the top would be anchored in space. The centrifugal force from the rotation of the planet would pull the top of the elevator outward, counteracting the force of gravity and keeping the elevator suspended.

## 3. What are the potential benefits of a gravitational elevator?

A gravitational elevator could potentially revolutionize space travel by providing a more efficient and cost-effective way to transport objects and people into space. It could also reduce the need for rockets and decrease the environmental impact of space launches. Additionally, it could open up new opportunities for space exploration and colonization.

## 4. What are the challenges of building a gravitational elevator?

One of the main challenges of building a gravitational elevator is finding a material strong enough to support its own weight and the weight of objects being transported. The cable or tower would need to be able to withstand immense tension and stress. Another challenge is finding a way to safely transport objects from the base of the elevator to the top without them getting damaged by the Earth's atmosphere.

## 5. Is a gravitational elevator possible?

Although the concept of a gravitational elevator has been studied for decades, it is still considered a theoretical concept and has not yet been successfully built. While there are still many technical challenges to overcome, some scientists believe that with advancements in technology and materials, a gravitational elevator could one day become a reality.

Replies
5
Views
2K
Replies
3
Views
2K
Replies
30
Views
2K
Replies
8
Views
9K
Replies
12
Views
3K
Replies
5
Views
1K
Replies
10
Views
1K
Replies
1
Views
1K
Replies
7
Views
19K
Replies
4
Views
2K