Pole vaulter landing on a mat

[bane32]

Homework Statement

Len is a 60 kg pole vaulter and he falls from a peak height of 5.4 meters after pole-vaulting over the crossbar set at that height. He lands on a thick mat and when he first makes contact with the mat, his centre of gravity is only 1.08 meters high. During Len's impact with the mat, it undergoes a maximum compression when his vertical velocity reaches 0 m/s and his centre of gravity is only 0.5 meters high. What is the magnitude (ignore direction) of the average force in Newtons exerted by the mat on Len during this impact?

Relevant Equations

Not exactly sure which ones to use for this.

I know that PE=mgh, SE=1/2(k)( x squared) and KE=1/2(m)(v squared)

Need to find normal force from the mat.

 

[BvU]

Hello @bane32 ,

!​

Homework Statement:: Len is a 60 kg pole vaulter and he falls from a peak height of 5.4 meters after pole-vaulting over the crossbar set at that height. He lands on a thick mat and when he first makes contact with the mat, his centre of gravity is only 1.08 meters high. During Len's impact with the mat, it undergoes a maximum compression when his vertical velocity reaches 0 m/s and his centre of gravity is only 0.5 meters high. What is the magnitude (ignore direction) of the average force in Newtons exerted by the mat on Len during this impact?
Relevant Equations:: Not exactly sure which ones to use for this.

I know that PE=mgh, SE=1/2(k)( x squared) and KE=1/2(m)(v squared)

Need to to find normal force from the mat.

Sounds like a good idea. However, I don't see a relevant equation with a force in it ? Do you know one ?

$\$

 

[bane32]

I know that his starting PE=3175.2 J based on his starting height of 5.4 meters above the ground. I know that as he falls, his PE gets converted to KE. It seems like when he first hits the mat at 1.08 m, his KE=3175.2 - (60)(9.8)(1.08)=2540.16 J.

What's throwing me off is what to do afterwards. The question mentions compression which I think would use the spring energy equation. But I'm lost for finding the normal force exerted by the mat in Newtons.

 

[BvU]

All very nice, but I still do not see a relevant equation featuring a force ...

 

[BvU]

Homework Statement:: ... What is the magnitude (ignore direction) of the average force in Newtons exerted by the mat on Len during this impact?
...
Need to find normal force from the mat.

The question mentions compression which I think would use the spring energy equation

Why not make life a little simpler: the exercise asks for an average force --- there is no spring aspect in this very inelastic 'collision'. Assume the mat exerts a constant force.

$\$

 

[haruspex]

I know that his starting PE=3175.2 J based on his starting height of 5.4 meters above the ground. I know that as he falls, his PE gets converted to KE. It seems like when he first hits the mat at 1.08 m, his KE=3175.2 - (60)(9.8)(1.08)=2540.16 J.

Ok, so you have calculated a KE, you are given a distance to stop in, and you are asked for a force. Does that jog your memory?
But be careful... gravity doesn’t suddenly switch off when he touches the mat.

There is one flaw with the problem, which @BvU knows I will leap on:

What is the magnitude (ignore direction) of the average force in Newtons exerted by the mat on Len during this impact?

You do not have enough information to calculate the average force. The question should say "what is the force, given that it is constant". If you were to assume a spring (but which doesn't expand again after being compressed), you would get a different answer.