How Is Work Calculated When Pulling a Blimp with Drag and Angle Considerations?

[hganser]

A blimp of mass 110 kg is pulled at an angle of 52 degrees downwards with respect to the horizontal for D=7 km on level ground at a constant velocity v=14 m/s. If the coefficient of drag (K in F=Kv^2) is 0.5 kg/m, how much work is done by the person pulling?

I know how to find work with the (1/2)mv^2 formula and the Fdcos(angle) formula. But I don't know how to apply the drag into either equation.

Do I just solve for F in the coefficient of drag equation then apply it? Or are there more steps?

 

[LowlyPion]

Welcome to PF.

This question is trying to get you to think about the work performed.

The blimp is not changing altitude so no change in potential energy ... so no work there.

It is moving at constant velocity, so no acceleration and no change in kinetic energy. No work there either, eh?

So where could the work be?

Could it be the force to overcome drag taken over the distance of 7 km?

 

[hganser]

Would that be using the equation they give me?
How would I find the work it takes to overcome the drag?
And the blimp is changing altitude. It is going downward at an angle.

 

[LowlyPion]

Would that be using the equation they give me?
How would I find the work it takes to overcome the drag?
And the blimp is changing altitude. It is going downward at an angle.

What is work?

Force over a distance. F of drag over the 7 km. They give you the v so figure the Force of the drag. Since I read it as the blimp being pulled horizontally at constant altitude, then that drag is in the direction against which the person/truck is moving and it is the horizontal component of the tension in the cable. For figuring work isn't this then the force to be taken over the distance traveled?

As to varying altitude, I don't see that in the problem statement. I see the angle at which it is being pulled, but unless there is more to the statement of the problem I think it is at constant altitude over the distance of 7 km.

Now I see that you might read it as the blimp being pulled downward for 7 km*Sin52°, but the comment about level ground suggests otherwise. Moreover, the force against which you would be operating is not gravity, but the net buoyant force of the blimp that I don't see enough information to figure, especially given changes in atmospheric pressure over that distance.