# Can Calculating a Horse's Leg Spring Constant Predict Jump Heights?

• Liz Hoyt
In summary, the student is trying to determine the spring constant for a horse's leg in order to calculate the potential energy stored in that leg. However, there may be some errors in the calculations and equations being used. It is important to include units in the calculations and consider the relationship between force and displacement. Once the spring constant is determined, it can be used to calculate the potential energy in the leg during a jump.
Liz Hoyt
Science fair help needed! Horses use the energy stored in their tendons to help propel them over a jump- much like a spring. By determining the spring constant for the leg, the student wants to then calculate the potential energy stored in that leg. Would this work? From her research proposal:
I will use the equation, PE=1/2kx² to find the potential energy the leg stores (where k=spring constant, x=spring displacement). X will be found by measuring the smallest distance between the two measuring points when the horse has both feet on the ground and subtracting from equilibrium. k can be solved for by using the equation; k= (x-x₁)/F. x being the displaced length, x₁ being leg at equilibrium and F equaling force. The values I will be using for that equation will be x equaling leg being stood on, x₁ relaxed leg, F being force on standing leg. To find force I will take the Weight of horse in kg then to find force on one leg, multiply by .55 (for forelimbs) or .45 (hindlimbs) then divide by two.
Does this make sense? The difference (x) between a leg at rest and under weight is 0.025m, Force is 1225N so spring constant is 0.00002041? This makes for a very small value for PE too?
I should include that I a biology teacher that is taking students to a state science fair. My background in physics is limited and the student is asking for help so I am seeking help on her behalf. Thank you!

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I'm not exactly sure what you did here. You were dealing with the potential energy of the spring, and then changed to the Hooke's law force.

If you are making a model of this via a simple spring problem, then I think there might be a few mistakes here. Here's what you need:

1. Get a value for the mass of a horse (in kg).
2. Figure out how high the horse needs to jump (in meters).
3. From 1 and 2, using PE = mgh, this is the minimum energy that you need to store in your spring (in Joules).
4. You know how much the horse's leg bends (your "displaced" length), (in meters).
5. Then, using the PE equation that you wrote, you have everything to calculate the spring constant.

You should never lose sight that these have units (something I often tell my students ad nauseum), even the spring constant. It is difficult to diagnose what went wrong with your description because you never included any units. We can't tell if you used the right ones, or if you mixed-and-matched different ones.

Zz.

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Liz Hoyt
ZapperZ said:
I'm not exactly sure what you did here. You were dealing with the potential energy of the spring, and then changed to the Hooke's law force.

If you are making a model of this via a simple spring problem, then I think there might be a few mistakes here. Here's what you need:

1. Get a value for the mass of a horse (in kg).
2. Figure out how high the horse needs to jump (in meters).
3. From 1 and 2, using PE = mgh, this is the minimum energy that you need to store in your spring (in Joules).
4. You know how much the horse's leg bends (your "displaced" length), (in meters).
5. Then, using the PE equation that you wrote, you have everything to calculate the spring constant.

You should never lose sight that these have units (something I often tell my students ad nauseum), even the spring constant. It is difficult to diagnose what went wrong with your description because you never included any units. We can't tell if you used the right ones, or if you mixed-and-matched different ones.

Zz.
She was hoping to determine the spring constant in the leg and then use that to determine the potential energy in that leg. I think that she has her formula for k incorrect though. It should be k=F/x with x being the displacement.

Liz Hoyt said:
She was hoping to determine the spring constant in the leg and then use that to determine the potential energy in that leg. I think that she has her formula for k incorrect though. It should be k=F/x with x being the displacement.

But think about it. Your "F" is nothing more than the weight of the horse. It ends up being a constant, no matter how high the horse has to jump, because your "equation" doesn't take this into account. The "x" is the displacement of the "spring", i.e. the horse's leg/muscles since you are modeling it as a spring. This is not the height it has to jump. So, does the fact that your F remains constant, no matter how high the horse has to jump, makes any sense to you?

Zz.

ZapperZ said:
But think about it. Your "F" is nothing more than the weight of the horse. It ends up being a constant, no matter how high the horse has to jump, because your "equation" doesn't take this into account. The "x" is the displacement of the "spring", i.e. the horse's leg/muscles since you are modeling it as a spring. This is not the height it has to jump. So, does the fact that your F remains constant, no matter how high the horse has to jump, makes any sense to you?

Zz.

Lets not consider the jump yet. If we are looking at determining the spring constant k, the force on the spring and the displacement are proportional. If we increase the force, we increase the displacement on the spring (x), right? In determining k, can't we use the displacement between a leg at rest (non-weight bearing) and the leg under the force of its weight. The difference in x (and there is one) is a result of the force of the horse's weight. We aren't even looking at the jump yet. Once she knows the spring constant, can she use the spring constant and the changes in displacement that occur as you alter jump height to determine the PE? Can't she look at the Potential Energy by measuring the varying displacements that occur as she alters jump height? Let's say the displacement on the spring is 0.05m for a 2' jump and 0.08 for a 4' jump. Knowing the spring constant is constant, and by measuring displacement, can she use PE = 1/2 k * x squared to determine how the horse compresses the spring in his tendons to handle varying jump heights?
and thank you ZapperZ for taking the time to allow me to hash this out with you! I really am appreciating this!

Liz Hoyt said:
Lets not consider the jump yet. If we are looking at determining the spring constant k, the force on the spring and the displacement are proportional. If we increase the force, we increase the displacement on the spring (x), right? In determining k, can't we use the displacement between a leg at rest (non-weight bearing) and the leg under the force of its weight. The difference in x (and there is one) is a result of the force of the horse's weight. We aren't even looking at the jump yet. Once she knows the spring constant, can she use the spring constant and the changes in displacement that occur as you alter jump height to determine the PE? Can't she look at the Potential Energy by measuring the varying displacements that occur as she alters jump height? Let's say the displacement on the spring is 0.05m for a 2' jump and 0.08 for a 4' jump. Knowing the spring constant is constant, and by measuring displacement, can she use PE = 1/2 k * x squared to determine how the horse compresses the spring in his tendons to handle varying jump heights?

I don't understand. What ULTIMATELY is to be determined here? The "spring constant", or the height that the horse can jump? I.e. what are the given or known variables?

I read your first post, and I get the impression that you know the height that the horse has to jump, or can jump, and so you want to find the spring constant, i.e. what is essentially the property of the horse's muscle. If I'm right in my interpretation, than using the Hooke's law force is "working too hard" (to paraphrase Mary Boas from the book). Sticking only with the potential energy will be sufficient, as I've outlined in my post.

If not, then you have to explain clearly what exactly is being calculated or estimated here.

Zz.

## What is the science behind horse jumping?

The science behind horse jumping is a combination of physics and biomechanics. It involves understanding the forces and mechanics involved in the horse's movement and how they interact with the environment.

## How does a horse generate enough force to jump over obstacles?

A horse generates enough force to jump over obstacles through a combination of muscular power, momentum, and proper technique. The horse's hind legs act as the engine, pushing off the ground with a powerful thrust, while the front legs provide balance and direction.

## What factors affect a horse's ability to jump?

There are several factors that can affect a horse's ability to jump, including the horse's conformation, speed, strength, and technique. The quality of the footing and the height and width of the obstacles can also play a role in a horse's jumping ability.

## How does a horse land after a jump without injuring itself?

A horse is able to land safely after a jump due to its natural ability to absorb shock and distribute weight evenly. The horse's muscles, tendons, and ligaments work together to cushion the impact, and the horse's body also has built-in shock absorption mechanisms, such as the flexing of its joints and the compression of its spine.

## What are the potential risks of horse jumping?

The potential risks of horse jumping include injuries to the horse, such as strains, sprains, and fractures, as well as injuries to the rider, such as falls and concussions. Proper training, conditioning, and safety precautions can help minimize these risks.

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