(a) An airplane flies at constant speed along a
straight line at an angle of 30' with the
horizontal. The weight of the airplane is
80000 N and its engine provides a thrust of
100000 N in the direction of flight.
Determine the lift force perpendicular to the
airplane's wings and the force due to air
resistance opposite to the airplane's
direction of motion. Draw the free-body
diagram for the airplane. Identify the no-
work force from amongst the four forces
being exerted on the airplane.
lift is not perpendicular to wings but perpendicular to the apparent air velocity (direction of motion ). You got it right about drag.
Is the plane following a horizontal path with nose tipped up 30 degrees (or 30 minutes, I can not tell from your text) or is it climbing or diving?
Since lift is perpendicular to the direction of motion, it does no work.
To determine the lift force perpendicular to the airplane's wings and the force due to air resistance opposite to the airplane's direction of motion, we can break down the forces acting on the airplane:
1. Weight: The weight of the airplane is 80000 N, acting vertically downward due to gravity.
2. Thrust: The engine provides a thrust of 100000 N in the direction of flight, which we can decompose into two components. One component acts horizontally in the direction of motion, and the other component acts vertically since the plane is at an angle to the horizontal.
3. Lift: The lift force is generated perpendicular to the wings and opposes the weight of the airplane. Since the airplane is flying at a constant speed, the lift force must balance the weight. Therefore, the lift force is also 80000 N in the upward direction.
4. Air Resistance: The force due to air resistance opposes the airplane's direction of motion. Since the airplane is flying at a constant speed, the air resistance force must balance the thrust force. Therefore, the air resistance force is also 100000 N in the opposite direction of flight.
Here is a breakdown of the forces and their directions:
^
|
| Lift (80000 N)
|
---------------------------> (Direction of flight)
|
| Air Resistance (100000 N)
|
|
Weight (80000 N)
Now, to identify the no-work force from amongst the four forces:
The no-work force is the force that does not contribute to the work done on the airplane. In this case, the no-work force is the Lift force since it acts perpendicular to the direction of flight. The work done by the lift force is zero because the displacement is perpendicular to the force. The other three forces (Weight, Thrust, and Air Resistance) contribute to the work done on the airplane as they act in the direction of motion.
Therefore, in this scenario, the Lift force is the no-work force.