Average Net force and high jumpers

[barbiegirl42]

Homework Statement

A high-jumper with a mass of 65kg just clears a height of 2.13m and drops onto a 0.30m thick landing mat.
a) What average net force does the landing mat exert on the high jumper if it is compressed by 0.18m during landing?
b) What would be the effect on the force if the high-jumper were to land in sand that compresses only 5cm

I managed to figure out the potential energy to be= 1356.81J
and the Velocity = 6.46 ms/-1

Answers:
a) 7100N
b) 27,000J

Homework Equations

Ek=1/2mv²
Ep=mgh
W=Fs=Change in energy
F=ma
F=mg

The Attempt at a Solution

Cannot figure out average net force.
I've tried a lot of things and even tried working backwards from the answer and cannot get anywhere. I just would like to know how to figure the average net force and the second question with the given information.

 

[tms]

What forces act on the jumper?

 

[haruspex]

Welcome to the forum... but perhaps you have not read the guidelines.
You are supposed to post your attempt at a solution, as far as you could get. If you couldn't even get started, at least some insight into what is blocking you.

However, I do sympathise with you on this problem, since in my view the question is flawed.
Unless specifically stated otherwise, "average force" ought to mean an average over time: ∫F.dt/∫dt, which can also be written as Δp/Δt, i.e. the change in momentum divided by the elapsed time. The reason for this is that average acceleration is definitely defined as Δv/Δt, and average force ought to equal mass * average acceleration.

The posted question gives you no way to determine the duration of the landing. You could guess, perhaps, that the force increases linearly with degree of compression, as with a spring. But in order to get the given answer, you have to interpret it as the average over distance. This you would calculate as ∫F.ds/∫ds = ΔE/Δs, the change in energy divided by the displacement. This will in general give a different answer from average over time.

 

[tms]

I think the problem wants the solver to pretend the average force is a constant force, and to use the kinematics equations to find the acceleration.

 

[barbiegirl42]

I managed to find the potential energy and the velocity and I can't get any further than that. The thing is, this is included in the exercise in my book under mechanical energy. The chapter is teaching kinetic and gravitational potential energy so somehow it has to relate to this?
It says in the summary that potential energy is stored energy with the potential to allow work to be done. It may take many forms, including chemical and spring.
I don't know if any of this helps.
Also I can't really show my attempt at the question since I don't know how to attempt it or what equations to really use with the information provided.

 

[tms]

If you have calculated the potential energy, then you already know how that relates to the problem. Look at the jumper as a particle dropped from a height. What is it's speed when it hits the mat?

 

[barbiegirl42]

yeah but it asks for the mat and not the jumper and somehow i have to use the thickness and the compression of the mat to figure out the answer. I still am stuck on it and really all I need to help and for someone to explain how to do it

 

[haruspex]

yeah but it asks for the mat and not the jumper and somehow i have to use the thickness and the compression of the mat to figure out the answer. I still am stuck on it and really all I need to help and for someone to explain how to do it

You should not assume all the information given is necessary.
I gave quite a strong hint how to relate the energy to the force at the end of the penultimate sentence in post #3.

 

[barbiegirl42]

Yeah and I tried that equation and it seemed to not work and did not give the answer.

 

[haruspex]

Yeah and I tried that equation and it seemed to not work and did not give the answer.

It worked for me. Please post your working.

 

[HallsofIvy]

You say you have calculated potential energy. (where? At the top of the jump?) That potential energy has become kinetic energy at the end and must be dissipated: work (energy) equals force times distance. You know the energy that must be dissipated and you know the distance so you can solve for force.

 

[barbiegirl42]

You say you have calculated potential energy. (where? At the top of the jump?) That potential energy has become kinetic energy at the end and must be dissipated: work (energy) equals force times distance. You know the energy that must be dissipated and you know the distance so you can solve for force.

I calculated the potential energy which is at the top of the jump. I know it becomes kinetic energy at the bottom (that's how I figured out the velocity) so I tried solving for force:

W=Fs
1356.81=Fx2.13m
F=1356.81/2.13
F= 637N
^ Wrong Answer

 

[barbiegirl42]

It worked for me. Please post your working.

As my previous post has, I pretty much did the same thing and got the same answer.
I'm just getting more and more confused.
You told me change in energy/displacement
I did
1356.81/2.13 and got 637N, still the wrong answer.

 

[tms]

The displacement over which the force of the mat works is the amount of compression, not the height of the bar.

 

[barbiegirl42]

The displacement over which the force of the mat works is the amount of compression, not the height of the bar.

Still did not work.

1356.81/0.18
= 7537.83 - close but still not the answer.

 

[tms]

Show your equations. I don't know what those numbers are, or how you got them.

 

[barbiegirl42]

Show your equations. I don't know what those numbers are, or how you got them.

If you saw above on the 3rd post the guy gave me a hint to what equation to use to find the force:
"But in order to get the given answer, you have to interpret it as the average over distance. This you would calculate as ∫F.ds/∫ds = ΔE/Δs, the change in energy divided by the displacement. This will in general give a different answer from average over time."
SO I did change in energy which I thin is 1356.81/0.18 (the compression of the mat) which did not give the right answer and I cannot really find the energy of the mat if I don't have the mass.

 

[haruspex]

SO I did change in energy which I thin is 1356.81/0.18 (the compression of the mat) which did not give the right answer and I cannot really find the energy of the mat if I don't have the mass.

The height of the bar from the ground is 2.13m. The mat lies on the ground, is 0.3m thick, and compresses 0.18m. What is the vertical distance between the bar and where the jumper comes to rest.

 

[tms]

If you saw above on the 3rd post the guy gave me a hint to what equation to use to find the force:
"But in order to get the given answer, you have to interpret it as the average over distance. This you would calculate as ∫F.ds/∫ds = ΔE/Δs, the change in energy divided by the displacement. This will in general give a different answer from average over time."
SO I did change in energy which I thin is 1356.81/0.18 (the compression of the mat) which did not give the right answer and I cannot really find the energy of the mat if I don't have the mass.

How did you get that number for the energy? What equations did you use? Show the actual equations, not just the numerical results.

 

[haruspex]

How did you get that number for the energy? What equations did you use? Show the actual equations, not just the numerical results.

It comes from using 2.13m as the vertical displacement (which is not quite right).

 

[tms]

It comes from using 2.13m as the vertical displacement (which is not quite right).

I know. I was trying to be Socratic.

 

[barbiegirl42]

Well if Ep at top=Ekat bottom
Then the change in energy has to be 1356.81
There is no equation really just simple logic. I used Ep=mgh to find that value.

 

[barbiegirl42]

Instead of arguing and asking me all these questions show me a equation that I can use and that will work and show me how it works, otherwise if I try to do the calculations using that equation and get something wrong and my answer turns out wrong then what am I supposed to do and you asking me questions ain't helping.

 

[haruspex]

Instead of arguing and asking me all these questions show me a equation that I can use and that will work and show me how it works, otherwise if I try to do the calculations using that equation and get something wrong and my answer turns out wrong then what am I supposed to do and you asking me questions ain't helping.

You have the equation but you are plugging in the wrong number for the height. You will get there if you answer my post #18.

 

[tms]

Well if Ep at top=Ekat bottom
Then the change in energy has to be 1356.81
There is no equation really just simple logic. I used Ep=mgh to find that value.

It really would help if you wrote out the equations. That way you should see more clearly what your mistake is. Just start with
$$E_{initial} = E_{final} + \Delta E$$
and then substitute expressions for the initial and final energy, being careful not to reuse the same variable for different values.

 

[tms]

Instead of arguing and asking me all these questions show me a equation that I can use and that will work and show me how it works, otherwise if I try to do the calculations using that equation and get something wrong and my answer turns out wrong then what am I supposed to do and you asking me questions ain't helping.

The purpose of the questions is to try to lead you to discover the solution on your own. You are more likely to understand and remember the solution when you get it yourself than when someone just hands it to you.

 

[barbiegirl42]

It really would help if you wrote out the equations. That way you should see more clearly what your mistake is. Just start with
$$E_{initial} = E_{final} + \Delta E$$
and then substitute expressions for the initial and final energy, being careful not to reuse the same variable for different values.

SO I managed to ask my physics teacher and he told me this:
The high jumper’s energy at the top of his path is purely potential (as you have determined).

When he hits the mat he is doing work on the mat to compress it. To do this work he must give up energy. His final energy when he finally stops is also purely potential. Be careful when working out his final potential energy as you have to use both the height of the mat and how much it was compressed to find his final height.

Once you know his final energy, the energy he “lost” has gone into the mat. And since change in energy = work = force x displacement, you can determine the force by using: energy lost by high jumper = force applied to mat x compression of mat. Rearrange for force and Bob’s you Uncle.

that is all I needed really. I was waiting for his reply and thought I would try out this website too, seems like teachers know what their doing. I only needed someone to explain to me simply what is going on and what equation to use. Thanks to him I got the answer

 

[haruspex]

To do this work he must give up energy. His final energy when he finally stops is also purely potential. Be careful when working out his final potential energy as you have to use both the height of the mat and how much it was compressed to find his final height.

Precisely what I pointed out to you in post #18. You were using the full 2.13m for the lost height, not subtracting the remaining thickness of the mat.
Also, don't forget that the question is essentially wrong - the 'average force' cannot really be calculated this way. I'd be interested in your teacher's answer to that.