# Newton's second law - jumping from a height

• eternalronin
In summary: If you don't bend your knees it could hurt - why do you think that is?When you jump from a height and try to land with your legs straight, you can experience a lot of pain because the force of the landing is greater than the force you exerted when jumping. If you bend your knees on landing, the force of the landing is equal to the force you exerted when jumping, and there is no pain. Why is this?
eternalronin

## Homework Statement

When jumping from a height on to a hard surface, it is advisable to bend one's knees on landing. How does bending the knees affect the time one takes to come to rest? (1 mark)

With reference to Newton's second law, explain why it is a good idea to bend one's knees. (2 marks)

F=ma

## The Attempt at a Solution

I'm not quite sure how to answer this question at all...

When landing, you need to change your momentum. What is the relationship between force, time, and change in momentum?
What is the difference between landing with legs straight and landing with them bent (and not held too rigidly) in terms of how forces change over time? Try to sketch a graph. What must the two graphs have in common?

With regards to the second part, you should make sure that you understand Newton's Second Law. More force acting upon a falling body is worse, whereas less force would be better, but how would bending your legs affect that force? Knowing the definitions of each component of F=ma should hopefully make the answer apparent.

haruspex said:
When landing, you need to change your momentum. What is the relationship between force, time, and change in momentum?
What is the difference between landing with legs straight and landing with them bent (and not held too rigidly) in terms of how forces change over time? Try to sketch a graph. What must the two graphs have in common?

Force is equal to rate of change in momentum? f=dp/dt I think. Well I don't know, do bent knees absorb force more? I'll try and draw graphs, thanks

AnTiFreeze3 said:
With regards to the second part, you should make sure that you understand Newton's Second Law. More force acting upon a falling body is worse, whereas less force would be better, but how would bending your legs affect that force? Knowing the definitions of each component of F=ma should hopefully make the answer apparent.

I'm not sure how bending your knees would change the force. Would it decrease it? And since mass stays constant, acceleration would decrease?

eternalronin said:
Force is equal to rate of change in momentum? f=dp/dt I think. Well I don't know, do bent knees absorb force more? I'll try and draw graphs, thanks

I'm not sure how bending your knees would change the force. Would it decrease it? And since mass stays constant, acceleration would decrease?

If you don't bend your knees it could hurt - why do you think that is?

Here is a fun way to learn:

Try to jump at least 10 times without bending your knees . (Do u experience any agony?)

Repeat the same experiment but this time bending your knees on every jump. (Feel Relaxed ? )

That is, if after jumping fro a height 10 times without bending your knees, you can do the same bending your knees!

haruspex said:
If you don't bend your knees it could hurt - why do you think that is?

I'm not sure where I was going with the 'acceleration would decrease thing' since it's always going to be 9.8, I think

I have an idea, is it because when the legs are bent the angle is different, so the component of the force going downwards is going to be smaller?

And also, when knees are bent it takes a longer time to decelerate, and there would be more displacement as the body is still moving lower. And since it takes a longer time to decelerate to 0, f=ma so the force would be lower?

## 1. What is Newton's second law?

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be, and the more massive the object, the less it will accelerate.

## 2. How does Newton's second law apply to jumping from a height?

When jumping from a height, Newton's second law applies because the force of gravity is acting on the person, causing them to accelerate towards the ground. The force of gravity is equal to the person's mass multiplied by the acceleration due to gravity (9.8 m/s^2). As the person falls, they also experience air resistance, which can affect their acceleration.

## 3. How does mass affect a person's jump from a height?

According to Newton's second law, mass and acceleration have an inverse relationship. This means that the more massive an object is, the less it will accelerate when a force is applied to it. In the case of jumping from a height, a person with a larger mass will not jump as high as a person with a smaller mass, given the same amount of force applied.

## 4. How does force affect a person's jump from a height?

Force is directly proportional to acceleration, according to Newton's second law. This means that the greater the force applied to an object, the greater its acceleration will be. In the case of jumping from a height, the force of the person pushing off the ground contributes to their upward acceleration, allowing them to jump higher.

## 5. What other factors besides mass and force can affect a person's jump from a height?

Other factors that can affect a person's jump from a height include air resistance, which can reduce the person's acceleration, and the person's technique and strength, which can determine the direction and strength of the force applied. Additionally, external forces such as wind or the surface of the ground can also play a role in the person's jump.

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