Angular Velocity and Acceleration for Elevator Mechanism

In summary, the problem involves an old-style elevator connected to a counterweight by a cable passing over a rotating disk. The disk must turn at 0.82 rpm to raise the elevator at a velocity of 15.0 cm/s. To start the elevator moving, it must be accelerated at 1/8g, and the angular acceleration of the disk must be found to be in rad/s^2. The disk must turn through a certain angle in radians and degrees when raising the elevator 3.10m between floors.
  • #1
YamiBustamante
17
0

Homework Statement


In a charming 19th-century hotel, an old-style elevator is connected to a counterweight by a cable that passes over a rotating disk 3.50m in diameter (the figure (Figure 1) ). The elevator is raised and lowered by turning the disk, and the cable does not slip on the rim of the disk but turns with it.

a) At how many rpm must the disk turn to raise the elevator at 15.0cm/s ?

b) To start the elevator moving, it must be accelerated at 1/8g. What must be the angular acceleration of the disk, in rad/s^2?

c) Through what angle (in radians ) has the disk turned when it has raised the elevator 3.10m between floors?

d) Through what angle (in degrees ) has the disk turned when it has raised the elevator 3.10m between floors?

Homework Equations


E = (1/2)Iw^(2)
I = (1/2)mR^(2)
w = v/R

The Attempt at a Solution


I tried using w = v/R but it didn't work! I even converted it to rpm but got the wrong answer!
 

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  • #2
YamiBustamante said:
I tried using w = v/R but it didn't work! I even converted it to rpm but got the wrong answer!
YamiBustamante said:
a) At how many rpm must the disk turn to raise the elevator at 15.0cm/s ?

Post your work, please. Keep in mind that rpm is revolutions per minute. The velocity you are given is in cm/s.
 
  • #3
AlephNumbers said:
Post your work, please. Keep in mind that rpm is revolutions per minute. The velocity you are given is in cm/s.
I made a calculation mistake! The answer is 0.82 rpm
 
  • #4
YamiBustamante said:
I made a calculation mistake! The answer is 0.82 rpm
So is this thread done, or do you still have questions?
 
  • #5
haruspex said:
So is this thread done, or do you still have questions?
It's done :D
 

FAQ: Angular Velocity and Acceleration for Elevator Mechanism

1. What is angular velocity and acceleration in relation to elevator mechanisms?

Angular velocity and acceleration are measures of how fast and how much an object is rotating around a fixed axis. In the case of elevator mechanisms, these measures refer to the speed and rate of change of the elevator's rotation around its axis, which is typically the elevator shaft.

2. How do angular velocity and acceleration affect the movement of elevators?

Angular velocity and acceleration play a crucial role in determining the speed and smoothness of an elevator's movement. The higher the angular velocity, the faster the elevator will rotate and move towards its destination. Similarly, a higher angular acceleration will result in a quicker change in the elevator's rotation, leading to a faster change in its speed and direction.

3. What factors can affect the angular velocity and acceleration of elevators?

The angular velocity and acceleration of elevators can be affected by various factors, including the weight and load of the elevator, the design and condition of the elevator mechanism, and external forces such as wind or vibrations. These factors can impact the smoothness and speed of the elevator's movement, and it is crucial to consider them in the design and maintenance of elevator systems.

4. How do engineers calculate and control the angular velocity and acceleration of elevators?

Engineers use mathematical equations and principles of physics, such as Newton's laws of motion and rotational dynamics, to calculate and control the angular velocity and acceleration of elevators. They also use various control systems and mechanisms, such as motors and brakes, to regulate and adjust the elevator's movement to achieve the desired velocity and acceleration.

5. What are some real-life applications of understanding angular velocity and acceleration in elevator mechanisms?

Understanding angular velocity and acceleration in elevator mechanisms is essential for the safe and efficient operation of elevators, which are crucial in modern buildings and infrastructure. It also has practical applications in other fields, such as robotics and manufacturing, where rotational motion and control are necessary for precise and controlled movement of objects.

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