Compare Net Work Done During Plane Dive & Climb

[klopez]

A plane is diving toward the ground and then climbs back upwards as shown below. A lift force acts perpendicular to the plane's displacement, s = 1.7 x 10$$^{3}$$ m, which should be taken to be the same for each case. The engines of the plane exert a thrust as shown which has the same magnitude during the dive and climb. The plane's weight is 5.9 x 10$$^{4}$$ N.

A) Is the total net work done by all the forces greater during the dive or the climb? Explain your answer.

B) Find the difference in the total net work done between the dive and the climb.

A picture of the situation is attached.


I am not sure how to start this problem. Should I break my force of gravity into components?

I have an exam tomorrow, so if this can be answered soon it would be greatly appreciated.

Thanks,

Kevin

 

[rock.freak667]

I believe that you should break it into components, one should act in the opposite to the lift while the other acts opposite to the thrust

 

[Moetasim]

I would first start by analyzing the forces acting on the plane during both the dive and climb. In this case, we have the lift force, thrust force, and weight of the plane. I would also break the weight force into components, one acting parallel to the plane's displacement and one acting perpendicular to it. This will help in understanding the work done by each force.

A) To determine the total net work done, we need to consider the work done by all the forces on the plane. The work done by the lift force is zero since it acts perpendicular to the displacement. The work done by the thrust force is also zero since it acts parallel to the displacement. This leaves us with the work done by the weight force. During the dive, the weight force is acting in the same direction as the displacement, thus it does positive work. However, during the climb, the weight force is acting in the opposite direction to the displacement, thus it does negative work. Therefore, the total net work done by all the forces is greater during the dive.

B) To find the difference in the total net work done, we need to calculate the work done by the weight force during both the dive and climb. During the dive, the weight force does positive work, which can be calculated as W = Fd = (5.9 x 10^4 N)(1.7 x 10^3 m) = 1.003 x 10^8 J. During the climb, the weight force does negative work, which can be calculated as W = -Fd = -(5.9 x 10^4 N)(1.7 x 10^3 m) = -1.003 x 10^8 J. Therefore, the difference in the total net work done is 2.006 x 10^8 J.

In summary, the total net work done is greater during the dive compared to the climb due to the direction of the weight force. The difference in the total net work done is equal to twice the work done by the weight force, with opposite signs.