Power and Mass Question -- A helicopter accelerating and ascending

[yamm14]

Homework Statement

A helicopter initially moving at 20m/s at a height of 50m above the ground accelerates to a speed of 41m/s and a height of 1300m in 140s. The power output of the helicopter is measured to be 460000W. What is the mass of the helicopter?

Relevant Equations

Power=change in energy/time or work/time
Potential Energy = (mass)(gravity)(height)
Kinetic Energy = (1/2)(mass)(speed squared)
Initial Energy = Final Energy
Total Energy = Kinetic Energy + Potential Energy

I started with calculating the Ep and Ek of the helicopter and got this:
Epi = 490m Eki= (1/2)(400m)
Epf = 12740m Ekf = (1/2)(1681m)

I don't really know where to go from there. Do the unknown mass variables cancel out? I'm lost!

 

[berkeman]

You have most of what you need in your post of the Relevant Equations (thank you for being so complete). What are the initial KE and PE of the craft? And the final values? Then what should you do?

 

[yamm14]

okay, I used the power = change in energy/time equation and got this:

Ei = 510m
Ef = 13580.5m

Change in energy = 13070.5m

460000 = 13070.5m/140s
460000 = 93.4m
m = 4925.1kg

I'm not sure if this is right.

 

[berkeman]

okay, I used the power = change in energy/time equation and got this:

Ei = 510m
Ef = 13580.5m

Change in energy = 13070.5m

460000 = 13070.5m/140s
460000 = 93.4m
m = 4925.1kg

I'm not sure if this is right.

Sorry, that makes no sense from the units perspective. Energy is measured in Joules, not in meters. Potential energy depends on mgh (what units for each?), and kinetic energy depends on mv^2/2 (what units for each?). Can you please post corrected equations and carry units in each calculation? That's the best way to keep your work organized and consistent. Thanks.

 

[gneill]

I suspect that the m's in the OP's equations are meant to represent the unknown mass of the helicopter, rather than meters. Although, I don't understand the values that he's arrived at. Definitely some clarification of the method used is needed.

 

[jbriggs444]

I started with calculating the Ep and Ek of the helicopter and got this:
Epi = 490m Eki= (1/2)(400m)
Epf = 12740m Ekf = (1/2)(1681m)

As others have suggested - show your work. Quoting numbers without explaining how you obtained them does not let us spot errors.

That said, let us try to reconstruct things.

Initial potential energy (Epi) = 490m. That looks like mgh where g = 9.8 m/s² and h = 20 meters. Sounds right.

Initial kinetic energy (Eki) = 1/2 400m. That looks like 1/2 mv² where v = 20 m/s². Again, that sounds right.

Final potential energy = 12740m. That looks like mgh where g = 9.8 m/s² and h=1300 meters. Good.

Final kinetic energy = 1/2 1681m. That looks like 1/2 mv² where v = 41 m/s². Good.

So we can erase the doubts about how those figures were arrived at.

 

[gneill]

So we can erase the doubts about how those figures were arrived at.

If the OP doesn't show the work, I think not.