A fully loaded Cessna-182 airplane of mass 1250 kg has an engine failure when flying with an airspeed of 129 km/h at an altitude of 2670 m on a calm day. It then glides at a constant glide angle (which is the direction of flight below the horizontal) towards a safe landing at this constant speed of 129 km/h experiencing a drag force of 1300 N that opposes the direction in which the plane is moving.
1.The lift force which acts perpendicular to the wings of the plane.
2.The rate with which the loaded plane is losing gravitational potential energy.
3.The rate with which the loaded plane is losing gravitational potential energy
1. The lift force is mass*g if the aircraft is at constant speed downward gliding.
2. rate losing PE?
altitude= vertical speed*time=
= speedgiven*sinGlideAngle*time
rate of altitude loss= speedgiven*sinGlideAngle
rate of PE loss: mg*rateOfAltitudeLossAbove.
Lift does not act perpendicular to the wings but to the oncoming air flow. The two angles differ by the angle of attack.
speed = 129*10^3/3600 = 35.8 m/s
weight = 1250 * 9.81 = 12,263 N
Path at angle T down from Horizontal
Vertical forces:
weight down = 12,263 N
Lift component up = L cos T
Drag component up = 1300 sin T
so
12,263 = L cos T + 1300 sin T
Horizontal forces:
weight not horizontal
Lift forward = L sin T
drag back = 1300 cos T
so
1300 cos T = L sin T
I agree with Damon, I was thinking the drag force as horizontal.
By the way, this means that for a glider:
Drag/Lift = tangent of steady glide angle
To find the answers to these questions, we need to apply relevant physics principles. Let's break them down one by one:
1. The lift force: The lift force acting on the plane can be determined using the equation for lift force: Lift = Weight = m * g, where m is the mass of the plane and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this scenario, the weight acts opposite to the lift, so the lift force also acts in the upward direction. Hence, the lift force would be equal to the weight, which is given as the mass of the plane multiplied by the acceleration due to gravity.
2. The rate with which the loaded plane is losing gravitational potential energy: The rate at which an object loses gravitational potential energy can be calculated using the equation: Power = Force * Velocity, where Force is the opposing force acting on the object and Velocity is the speed at which the object is moving. In this case, the opposing force acting on the plane is the drag force, given as 1300 N, and the velocity of the plane is given as 129 km/h.
To convert the velocity from km/h to m/s, we can multiply it by (1000 m / 3600 s) to get the velocity in m/s. Once we have the velocity in m/s, we can calculate the power using the equation mentioned above.
3. The rate with which the loaded plane is losing gravitational potential energy: To calculate the rate at which the loaded plane is losing gravitational potential energy, we need to multiply the power obtained in the previous step by the gravitational potential energy lost in each unit of time, i.e., the rate. Since the power is the rate at which energy is transferred, multiplying it by time would give us the energy lost.
I hope this helps in understanding how to approach and calculate these values.