What is the solution to the cow tipping problem?

  • Context: Graduate 
  • Thread starter Thread starter asadpasat
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the "cow tipping problem," focusing on the mechanics involved in determining the forces and angles necessary for tipping a cow. Participants explore the mathematical relationships and physical principles underlying the problem, including lever equations and the geometry of the situation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant describes a method for analyzing the cow tipping problem using a rectangle around the cow's body and a diagonal to find the center of mass.
  • Another participant requests clarification on the cow tipping problem, indicating a need for a diagram and a clear statement of the problem.
  • It is noted that the cow-tipper applies force at the top corner of the cow, pushing perpendicular to the diagonal, and the lever-arm for the gravitational force is identified as x/2.
  • Concerns are raised about the necessity of including "a" in the equations, with some participants questioning its role in maintaining dimensional consistency.
  • Some participants express differing opinions on the approach to solving for x/2, with suggestions to simplify the process by using x/2 directly instead of involving cosine functions.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of certain variables in the equations and the approach to solving the problem. There is no consensus on the best method or the role of "a" in the calculations.

Contextual Notes

Participants highlight potential confusion regarding the geometric relationships and the application of trigonometric functions in the context of the problem. The discussion reflects varying levels of understanding and approaches to the mathematical modeling involved.

asadpasat
Messages
41
Reaction score
1
So I saw the cow tipping problem and I am having trouble figuring out how they got to the final equation.
Imagine making a rectangle around a cows body. Making a diagonal across the rectangle and center of mass being in center of the diagonal. One half of the diagonal is "a", and second is "b". Angle between the ground and the diagonal is theta. Drawing a Fg from center of mass divides the bottom line of rectangular in half (x/2)
From lever equation: (Fe)(de)=(Fl)(dl)
Transforming it: (F)(a+b)= (Fl)(dl)
(F)(a+b)= mg a cosθ [ I don't understand why is "a" necessary]
cosθ= (x/2)/a
(F)(a+b)= mg a ((x/2)/a)
(F)(a+b)= mg (x/2)
(F)= (mg (x/2)) / (a+b)
 
Physics news on Phys.org
OK, I'll bite. What's the "cow tipping problem"? A diagram and statement of the problem would be nice.
 
The cow-tipper is pushing with strength Fe , applied to the cow at the top corner, pushing in the optimal direction (perp. to the diagonal).
in line 3, the "lever-arm" for the gravity Force (that is, distance from pivot perp. to the weight vector) is x/2
 
lightgrav said:
The cow-tipper is pushing with strength Fe , applied to the cow at the top corner, pushing in the optimal direction (perp. to the diagonal).
in line 3, the "lever-arm" for the gravity Force (that is, distance from pivot perp. to the weight vector) is x/2
Got it. Thanks!
 
asadpasat said:
(F)(a+b)= mg a cosθ [ I don't understand why is "a" necessary]
You need the perpendicular distance between mg and the pivot, which is "a cosθ". (Or x/2.) Without the "a" the equation would be dimensionally inconsistent.
 
Doc Al said:
You need the perpendicular distance between mg and the pivot, which is "a cosθ". (Or x/2.) Without the "a" the equation would be dimensionally inconsistent.
It seems like a long way from solving for (x/2) by cos, and then substituting cos, just to get (x/2).
 
asadpasat said:
It seems like a long way from solving for (x/2) by cos, and then substituting cos.
I would have went directly to x/2, since you were given that up front.
 
Doc Al said:
I would have went directly to x/2, since you were given that up front.
ok, great. Thanks
 

Similar threads

Undergrad Change of coordinates in a potential energy field
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Understanding the derivation for Elastic Potential Energy.
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Modeling the damping of a physical rigid pendulum
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Solving Sub-Problem for OpenAI Lunar Lander v2: Seeking Advice
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Solving Wheel Coming to a Stop: FBD, Friction & Hysteresis
  • · Replies 22 ·
Replies
22
Views
5K
Graduate Is there a better method to solve the Box Tipping on Inclined Plane problem?
  • · Replies 1 ·
Replies
1
Views
6K
Where on a rigid body is a resultant force applied?
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Calculate velocity of streams impinging at differing angles
  • · Replies 30 ·
2
Replies
30
Views
2K
Graduate Center of Mass of Non-Uniform Rod Using Piecewise-Defined Function?
  • · Replies 5 ·
Replies
5
Views
4K
What Is the Maximum Acceleration of a Crate Up an Incline Before Tipping Over?
  • · Replies 15 ·
Replies
15
Views
2K