Posted by Mary on Tuesday, February 27, 2007 at 10:37pm.
The drawing shows a plane diving towards the ground and then climbing back upward. During each of these motions, the lift force L acts perpendicular to the dispacement s, which has the same magnitude of 2.8 103 m in each case. The engines of the plane exert a thrust T, which points in the direction of the displacement and has the same magnitude during the dive and the climb. The weight W of the plane has a magnitude of 5.8 104 N. In both the motions, net force is performed due to the combined action of the forces L, T and W.
Find the difference between the net work done during the dive and the climb.
In the diagram
(a) Dive - T is going in the direction of the nose of the plane downward which is also the displacement s. L is perpendicular to T. W is heading north and is 75 degrees from T.
(b) Climb - T is going in the direction of the nose of the plane upwards which is also the displacement s. L is perpendicular to T. W is heading north and is 115 degrees from T.
Work done is force*displacment in the direction of net force. So the key here is to add the three forces as vectors and do the dot product with displacement to get work.
In the dive:
Net force=T + L + W
work=netforce dot displacment
= Ts + L dot s + W dot s
= Ts + zero + Ts + zero + Ws cosine( 90- dive angle)
= Ts + Ws sine dive angle
Where s is the displacement in a given time.
Now in the climb..
work=netforce dot displacment
= Ts + L dot s + W dot s
= Ts + zero + Ts + zero + Ws cosine( 90+ dive angle)
= Ts- Ws sine dive angle
So the difference between network done on the aircraft?
Workd-Workc= 2Ws sine of dive angle
Does "dot" means multiply?
Does "Ts" means thrust multiplied by displacement.
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