How Much Power Does a Climbing Person Develop?

[petuniac]

Question is.. how much power does a 45 kg person develop climbing up a vertical ladder 7.0 m high if the average acceleration is 0.25 m/s^2?

This is where I'm at... (so far anyways)

calculate t from d = vt + 1/2at^2 and get value of 7.5 s to climb ladder... but now, how do I calculate Work in order to sub into P=W/t equation...

I have tried this... W = (Fg + Fa)*d = [(45)(9.81) + (45)(0.25)]*7 = 3168.9

and then P= W/t = 3168.9/7.5 = 423 W

Answer in book is 423 W but I am confused as to why I am right.. don't Fg and Fa act in opposite directions on the FBD??

Any help is appreciated

 

[nrqed]

Question is.. how much power does a 45 kg person develop climbing up a vertical ladder 7.0 m high if the average acceleration is 0.25 m/s^2?

This is where I'm at... (so far anyways)

calculate t from d = vt + 1/2at^2 and get value of 7.5 s to climb ladder... but now, how do I calculate Work in order to sub into P=W/t equation...

I have tried this... W = (Fg + Fa)*d = [(45)(9.81) + (45)(0.25)]*7 = 3168.9

and then P= W/t = 3168.9/7.5 = 423 W

Answer in book is 423 W but I am confused as to why I am right.. don't Fg and Fa act in opposite directions on the FBD??

Any help is appreciated

The correct way to think about this is $F_{person} - m g = m a_y$ (where I am working in the y direction). So the force applied by the person is $F_{person} = mg + m a_y$ (makes sense, the person must apply a larger force than mg in order to accelerate upward). Now you multiply this by the distance to get the work done by the person.

Patrick

 

[kyle8921]

!

I can confirm that your calculations and approach are correct. The formula you have used, W = (Fg + Fa)*d, takes into account both the force of gravity (Fg) and the force applied by the person (Fa) while climbing the ladder. Both of these forces act in the same direction, so they can be added together.

The reason you may be confused about the direction of the forces is because in this case, we are only concerned with the magnitude of the forces, not their direction. The formula for power, P = W/t, also only considers the magnitude of the work done (W) and the time it takes (t), not the direction of the forces.

In summary, your calculations and reasoning are correct, and the answer of 423 W is the accurate amount of power that a 45 kg person would develop while climbing a 7.0 m ladder with an average acceleration of 0.25 m/s^2. I hope this helps clarify any confusion you may have had. Keep up the good work in your scientific calculations!