Two gear system in static equilibrium

In summary, the problem involves two solid steel shafts coupled together with meshed gears. The objective is to determine the angle of twist at end A, where one of the shafts (DC) is fixed at point D. The angle of twist can be calculated using the formula involving torque, shaft length, polar moment of inertia, and shear modulus. The sum of forces and moments on the system must equal zero for static equilibrium. The torque exerted on the system at point A is 45 Nm, and at point D it is -45 Nm. However, balancing forces at the meshed gears reveals that the torque at point D is actually -22.5 Nm, indicating that the torques must be about the same
  • #1
Jage
2
0

Homework Statement



Two solid steel shafts are coupled together using meshed gears. Determine the angle of twist of end A. Shaft DC is fixed at D.

Homework Equations



angle of twist = torque * shaft length / ( polar moment of inertia * shear modulus)

balance of forces where the two gears mesh:
150mm * Fab = 0.75mm * Fcd

The Attempt at a Solution



I know the solution, but am puzzled about what is wrong with the following approach:

The sum of forces and moments on the system must equal zero since the system is at static equilibrium. Since torque exerted on the system at A is 45Nm, the torque exerted on the system at D must therefore be -45 Nm.

However, balancing forces at where the two gears mesh shows that torque at D is really -22.5 Nm.
 

Attachments

  • Capture.PNG
    Capture.PNG
    9.4 KB · Views: 747
Physics news on Phys.org
  • #2
To balance torques, they must be about the same axis.
 

1. What is a two gear system in static equilibrium?

A two gear system in static equilibrium is a mechanical system where two gears are connected and exert equal and opposite forces on each other, resulting in a state of balance or stability. This means that the gears are not accelerating and are not rotating at different speeds.

2. How does a two gear system achieve static equilibrium?

A two gear system achieves static equilibrium when the forces exerted by each gear on the other are equal in magnitude and opposite in direction. This means that the gears are in a state of balance and will not rotate or accelerate. The teeth of the gears interlock and prevent them from slipping, allowing them to maintain a constant distance from each other.

3. What factors affect the static equilibrium of a two gear system?

The factors that affect the static equilibrium of a two gear system include the size and shape of the gears, the number of teeth on each gear, the distance between the gears, and the materials used to make the gears. These factors can impact the amount of force needed to maintain equilibrium and the overall stability of the system.

4. How is a two gear system used in real-world applications?

A two gear system is commonly used in many mechanical devices and machines, such as bicycles, automobiles, and industrial machinery. It allows for the transfer of power and motion between two rotating shafts while maintaining a constant speed ratio. This makes it a crucial component in many everyday devices and industries.

5. What are the advantages of using a two gear system in static equilibrium?

The advantages of using a two gear system in static equilibrium include its simplicity, efficiency, and stability. It also allows for the transfer of power and motion between two rotating shafts without the need for additional components. Additionally, the gears can be designed and arranged in various ways to suit different applications, making it a versatile and reliable mechanism.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
974
  • Introductory Physics Homework Help
Replies
5
Views
922
  • Introductory Physics Homework Help
Replies
32
Views
975
  • Introductory Physics Homework Help
Replies
13
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
11K
Replies
17
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
2K
Back
Top