Equation for sum of torques on a ladder and minimum angle

In summary, the equation for calculating the sum of torques on a ladder is Στ = mgLsinθ, where Στ is the sum of torques, m is the mass of the ladder, g is the acceleration due to gravity, L is the length of the ladder, and θ is the angle between the ladder and the ground. The minimum angle a ladder can make with the ground without slipping can be determined by setting the sum of torques equal to zero and solving for θ, where the sine of the angle is equal to the coefficient of static friction between the ladder and the ground. The sum of torques is affected by the mass of the ladder, the length of the ladder, the angle between the
  • #1
Howard Fox
38
2

Homework Statement


upload_2018-12-3_17-6-53.png
[/B]
upload_2018-12-3_17-10-32.png

upload_2018-12-3_17-13-19.png

Homework Equations


Drawing a diagram for the forces is the easy part. I am not sure I am doing the equation of the sum of the torques well.

The Attempt at a Solution


This is my attempt for the forces[/B]
upload_2018-12-3_17-35-22.png

And this for the torques:
upload_2018-12-3_17-57-34.png
 

Attachments

  • upload_2018-12-3_17-6-53.png
    upload_2018-12-3_17-6-53.png
    29.1 KB · Views: 536
  • upload_2018-12-3_17-10-32.png
    upload_2018-12-3_17-10-32.png
    11.3 KB · Views: 555
  • upload_2018-12-3_17-13-19.png
    upload_2018-12-3_17-13-19.png
    6.6 KB · Views: 499
  • upload_2018-12-3_17-35-22.png
    upload_2018-12-3_17-35-22.png
    10.6 KB · Views: 503
  • upload_2018-12-3_17-57-34.png
    upload_2018-12-3_17-57-34.png
    16.9 KB · Views: 470
Physics news on Phys.org
  • #2
If you calculate torques about the point of contact with the ground, there are 3 torques to consider not just 2. You missed the torque generated by ##F_{f2}## at the point of contact with the wall.
 

What is the equation for calculating the sum of torques on a ladder?

The equation is Στ = mgLsinθ, where Στ is the sum of torques, m is the mass of the ladder, g is the acceleration due to gravity, L is the length of the ladder, and θ is the angle between the ladder and the ground.

How do you determine the minimum angle a ladder can make with the ground without slipping?

The minimum angle can be determined by setting the sum of torques equal to zero and solving for θ. The minimum angle is when the sine of the angle is equal to the coefficient of static friction between the ladder and the ground.

What factors affect the sum of torques on a ladder?

The sum of torques is affected by the mass of the ladder, the length of the ladder, the angle between the ladder and the ground, and the coefficient of static friction between the ladder and the ground.

Can you use the equation for sum of torques on a ladder for any type of ladder?

Yes, the equation can be used for any type of ladder as long as the ladder is in equilibrium and there is no external force acting on it.

How does the sum of torques on a ladder change when the ladder is not in equilibrium?

If the ladder is not in equilibrium, the sum of torques will not be equal to zero. In this case, the ladder will either start to slip or rotate, and the equation for sum of torques will no longer be valid. Other forces, such as friction or external forces, may need to be considered in the calculation.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
475
  • Introductory Physics Homework Help
Replies
22
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
315
  • Introductory Physics Homework Help
2
Replies
42
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
211
  • Introductory Physics Homework Help
Replies
1
Views
790
Replies
6
Views
749
  • Introductory Physics Homework Help
Replies
7
Views
177
Back
Top