Work, Energy, Power Problems: No Mass? No Speed?

[harujina]

Homework Statement

Athletes who compete in downhill skiing try to lose as little energy as possible. A skier starts from rest at the top of a 65 m hill and skis to the bottom as fast as possible. When she arrives at the bottom, she has a speed of 23 m/s. Calculate the skier's efficiency. Explain why the mass of the skier is not required when calculating the efficiency.

Homework Equations

Eg = mgh

The Attempt at a Solution

I don't understand since Eg = mgh, and I'm only given height and velocity. How could I possibly find the skier's efficiency without mass?

*Also, another question asks how I could determine power without time. How is this possible when P = E/t?

 

[haruspex]

Just put the mass in as an unknown m and plod through the equations. See what happens.
For the other question, you need to post it in full.

 

[smokiee]

Since mass is unknown so put mass as unknown, at the end the mass will cancel out because Eout/Ein*100%...
Follow the steps
E input = mgh
mass= unknown, so E input= mass*9.8ms^-2*65m = 637m
E input = 637*mass

E out = E kinetic at bottom of hill, so Ek= (mv^2)/2
E out= 264.5*mass
Finally, Efficiency= Eout/Ein *100%
Efficiency= (264.5*mass)/(637*mass) * 100%
Since the mass is same, so they cancel out: it will not effect the answer...
Efficiency = 41.5%

 

[smokiee]

Just put the mass in as an unknown m and plod through the equations. See what happens.
For the other question, you need to post it in full.
[/QUOT

Homework Statement

Athletes who compete in downhill skiing try to lose as little energy as possible. A skier starts from rest at the top of a 65 m hill and skis to the bottom as fast as possible. When she arrives at the bottom, she has a speed of 23 m/s. Calculate the skier's efficiency. Explain why the mass of the skier is not required when calculating the efficiency.

Homework Equations

Eg = mgh

The Attempt at a Solution

I don't understand since Eg = mgh, and I'm only given height and velocity. How could I possibly find the skier's efficiency without mass?

*Also, another question asks how I could determine power without time. How is this possible when P = E/t?

https://www.physicsforums.com/threa...problems-no-mass-no-speed.721041/post-6471736

 

[haruspex]

Since mass is unknown so put mass as unknown, at the end the mass will cancel out because Eout/Ein*100%...
Follow the steps
E input = mgh
mass= unknown, so E input= mass*9.8ms^-2*65m = 637m
E input = 637*mass

E out = E kinetic at bottom of hill, so Ek= (mv^2)/2
E out= 264.5*mass
Finally, Efficiency= Eout/Ein *100%
Efficiency= (264.5*mass)/(637*mass) * 100%
Since the mass is same, so they cancel out: it will not effect the answer...
Efficiency = 41.5%

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