Stability: Leaning Horse against a Wall

In summary, this problem asks you to solve for the torque on a horse's feet due to a wall, and you find that the wall force is 1.43 times the weight of the horse.
  • #1
Jazz
103
5

Homework Statement


image.jpg


Data:

##m = 500\ kg##
Distances given in the image.

Homework Equations



##\tau = rF\sin(\theta)##

##F_{net} = ma##

The Attempt at a Solution



It seems this problem is intended to be one where torque applies, but I don't see it in that way. And of course my answer doesn't agree with that given by the textbook :).

The diagram:

image.jpg


According to my understanding, there is a component of the weight acting along the horse's body (the diagonal I've drawn) and another one perpendicular to its body, which is making it rotate to the left. I labeled the latter ##w_{\perp(horse)}##. The component of ##w_{\perp(horse)}## that lies perpendicular to the wall, I think, has the same magnitude that the force exerted by the wall on the horse. This is what I mean:

image.jpg


Then:

##w_{\perp(horse)} = w\sin(\theta)##

##F_{wall} = w_{\perp(horse)}\cos(\theta)##

##F_{wall} = w\sin(\theta)\cos(\theta)##

And by Newton's Third Law, this is the force exerted on the wall.

The angle is found to be ##14.04º##, so

##F_{wall} = 500\ kg \cdot 9.80\ m/s^2 \cdot \sin(14.04º) \cdot \cos(14.04º) = 1.15 \times 10^3 N##

Maybe it should have a negative sign since it's in the opposite direction, but that is not what I'm worried about. The textbook's answer is ##1.43 \times 10^3 N##. I have no idea what I'm missing /:.

Thanks !
 
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  • #2
You are over complicating this problem and getting messed up. Sum torques about the horses feet. Torque of a force is force times perpendicular distance.
 
  • #3
PhanthomJay said:
You are over complicating this problem and getting messed up. Sum torques about the horses feet. Torque of a force is force times perpendicular distance.

Ah, I see. I confused the perpendicular distance with the perpendicular component of the force (I've been doing so all the time :) ).

##\sum \tau = 0 = \tau_{ccw} - \tau_{cw}##

##\sum \tau = 0 = \tau_{weight} - \tau_{wall}##

##\tau_{wall} = \tau_{weight}##

##F_{wall} = \frac{500\ kg \cdot 9.80\ m/s^2 \cdot 0.35\ m}{1.20\ m}##

##F_{wall} = 1.43 \times 10^3\ N##

If I were to solve a similar problem where ##\sum F = 0##, I must then assume ##F_{wall} = friction ## and ##w = F_{normal}## about the horses feet, right? I want to be sure about it, because I also got confused with that and with the fact that the forces are acting along different heights/distances.
 
  • #4
Jazz said:
If I were to solve a similar problem where ##\sum F = 0##, I must then assume ##F_{wall} = friction ## and ##w = F_{normal}## about the horses feet, right? I want to be sure about it, because I also got confused with that and with the fact that the forces are acting along different heights/distances.
Yes, that is correct. Normal force from ground acts up on the horses feet equal in magnitude to its weight, and the ground friction force on its feet acts left , equal in magnitude to the normal wall force.
 
  • #5
PhanthomJay said:
Yes, that is correct. Normal force from ground acts up on the horses feet equal in magnitude to its weight, and the ground friction force on its feet acts left , equal in magnitude to the normal wall force.

Nice!

Thanks for helping me [:
 

1. How does the weight of the horse influence its stability when leaning against a wall?

The weight of the horse is a key factor in determining its stability when leaning against a wall. A heavier horse will have a lower center of gravity, making it more stable and less likely to tip over. On the other hand, a lighter horse may be more prone to tipping over if not properly balanced.

2. Can a horse maintain its balance when leaning against a wall for an extended period of time?

Yes, a horse can maintain its balance when leaning against a wall for an extended period of time. Horses have a strong sense of balance and are able to adjust their weight and stance to maintain stability. However, it is important to provide breaks and allow the horse to shift positions to prevent fatigue and discomfort.

3. What is the ideal angle for a horse to lean against a wall without losing its balance?

The ideal angle for a horse to lean against a wall without losing its balance is approximately 45 degrees. This allows for optimal weight distribution and minimizes the risk of the horse tipping over. However, the stability also depends on the surface of the wall and the strength of the horse's legs.

4. How does the surface of the wall affect the stability of a horse leaning against it?

The surface of the wall can greatly impact the stability of a horse when leaning against it. A smooth and solid surface, such as concrete, can provide more support and stability compared to a rough or uneven surface. It is important to choose a suitable wall surface to ensure the horse's safety.

5. Are there any potential risks involved with leaning a horse against a wall?

Yes, there are potential risks involved with leaning a horse against a wall. If the horse is not balanced properly or the wall is unstable, there is a risk of the horse tipping over. Additionally, if the horse is forced to lean against the wall for an extended period of time, it may experience discomfort or fatigue. It is important to monitor the horse and ensure its safety when leaning against a wall.

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