A jet plane is flying with a constant speed along a straight line, at an angle of 30.0° above the horizontal, as shown in part (a) of the drawing. The plane has a weight of magnitude 87500 N, and its engines provide a forward thrust . In addition, the lift force (directed perpendicular to the wings) and the force of air resistance (directed opposite to the motion) act on the plane. Part (b) of the drawing shows the free-body diagram of the plane. The air resistance has magnitude 60700 N. What are (a) the thrust and (b) the lift?
a) The thrust is 26800 N.
b) The lift is 56700 N.
To find the thrust and lift forces acting on the plane, we can analyze the forces acting on the plane along the horizontal and vertical axes separately.
(a) The thrust force acts along the horizontal axis and is responsible for the forward motion of the plane. No other forces act in this direction, so the thrust force is the only horizontal force.
Therefore, the thrust force = magnitude of the weight of the plane = 87500 N.
(b) The lift force acts perpendicular to the wings of the plane. To find its magnitude, we need to consider the vertical forces acting on the plane.
Taking the upward direction as positive, we have:
Sum of upward forces = lift force - weight of the plane
Sum of downward forces = magnitude of the air resistance
In equilibrium (constant speed), the sum of the upward and downward forces must be zero. So, we can set up the following equation:
lift force - weight of the plane = magnitude of the air resistance
Substituting the given values, we get:
lift force - 87500 N = 60700 N
To isolate the lift force, we rearrange the equation:
lift force = 87500 N + 60700 N
lift force = 148200 N
Therefore, (a) the thrust force is 87500 N, and (b) the lift force is 148200 N.
To find the thrust and lift of the plane, we need to break down the forces acting on the plane.
(a) The thrust is the force provided by the engines that propels the plane forward. Since the plane is flying at a constant speed, the thrust force must equal the force of air resistance.
Therefore, the thrust is equal to the magnitude of the force of air resistance, which is 60700 N.
(b) The lift force is perpendicular to the wings and is responsible for keeping the plane airborne. It acts in the upward direction.
To find the lift force, we need to resolve the weight of the plane into its components. The weight has a magnitude of 87500 N.
The vertical component of the weight is given by:
Vertical component = Weight * sin(angle)
Vertical component = 87500 N * sin(30°) = 43750 N
Since the lift force is equal in magnitude but opposite in direction to the vertical component of the weight, the lift force is also 43750 N.
Therefore, (a) the thrust is 60700 N, and (b) the lift is 43750 N.