Finding the Mass of a Pole Vault Athlete

[Bunny-chan]

Homework Statement

An olympic athlete with [itex]~30[/itex] kg mass is participating in pole vaulting. The athlete runs and, at the moment of the jump, he has a velocity of [itex]~10[/itex] m/s. Calculate the maximum height he can reach.

To solve these kinds of problems, we can just convert all the kinetic energy the athlete develops during the motion to gravitational potential energy, and find the point which it has zero kinetic energy. But what I'm having trouble with is to calculate the mass of the athlete given initial velocity and the maximum height.

2. Homework Equations

The Attempt at a Solution

Evidently, If I try to use the conservation of energy formula for the athlete [tex]\frac{1}{2}mV_0^2 = mgh[/tex]then the masses will just cancel each other and I won't go anywhere. Thanks for the help.

 

[gneill]

Doesn't the problem statement supply the mass? What does the problem ask you to find?

 

[Bunny-chan]

Doesn't the problem statement supply the mass? What does the problem ask you to find?

It asks me to find the mass based on the running velocity (10m/s) and the maximum height (5.2m/s). Do you think that maybe it was mistyped?

 

[gneill]

It asks me to find the mass based on the running velocity (10m/s) and the maximum height (5.2m/s). Do you think that maybe it was mistyped?

Are you looking at a different problem than the one you posted? Your problem statement says:

An olympic athlete with 30 kg mass is participating in pole vaulting. The athlete runs and, at the moment of the jump, he has a velocity of 10 m/s. Calculate the maximum height he can reach.

 

[Bunny-chan]

Are you looking at a different problem than the one you posted? Your problem statement says:

Yes, and then I said "But what I'm having trouble with is to calculate the mass of the athlete given initial velocity and the maximum height.". Sorry for the misleading information!

 

[Bunny-chan]

I edited the post.

 

[gneill]

If I understand what you are saying, it is not the original problem that you are having difficulty with but a different scenario where you are instead given the initial velocity and maximum height and then wish to deduce the mass?

If that is the case then the answer is that you cannot. Since both the kinetic energy and the gravitational potential energy are directly proportional to the mass, then when they are equated the mass cancels as you've noted. The same height would be achieved no matter what the mass is, so long as it had the same initial velocity.

In order to determine the mass you would need some other information relating the mass to the motion.

 

[Bunny-chan]

If I understand what you are saying, it is not the original problem that you are having difficulty with but a different scenario where you are instead given the initial velocity and maximum height and then wish to deduce the mass?

If that is the case then the answer is that you cannot. Since both the kinetic energy and the gravitational potential energy are directly proportional to the mass, then when they are equated the mass cancels as you've noted. The same height would be achieved no matter what the mass is, so long as it had the same initial velocity.

In order to determine the mass you would need some other information relating the mass to the motion.

Thank you very much! That's what I wanted to know.