a kite weighs 2.50 lb and has an area of 8 square-ft. The tension in the kite is 6.6 lb when the string makes an angle of 45degrees with the horizontal. For a wind of 20 mph, assume an angle of 8 degrees with the horizontal. Consider the kite essentially flat plate
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It seems strange that a wind would be 8 degrees from horizontal. Is that up or down from horizontal?
To solve this problem, we need to break it down into different parts:
1. Calculate the force of gravity acting on the kite.
2. Find the lift force acting on the kite.
3. Determine the resultant force on the kite.
4. Calculate the angle of inclination.
5. Calculate the wind force acting on the kite.
6. Determine the net force on the kite.
Let's go step by step:
1. Calculate the force of gravity acting on the kite:
The weight of the kite is given as 2.50 lb. The force of gravity acting on an object is equal to its weight. So, the force of gravity acting on the kite is 2.50 lb.
2. Find the lift force acting on the kite:
The lift force acting on the kite can be determined using the formula L = T * sin(θ), where L is the lift force, T is the tension in the kite, and θ is the angle between the string and the horizontal plane.
Given that the tension in the kite is 6.6 lb and the angle is 45 degrees, we can substitute these values into the formula:
L = 6.6 lb * sin(45°)
L = 6.6 lb * 0.7071
L ≈ 4.65 lb
So, the lift force acting on the kite is approximately 4.65 lb.
3. Determine the resultant force on the kite:
The resultant force on the kite is the vector sum of the gravitational force and the lift force. Since the forces act in opposite directions, we subtract the lift force from the force of gravity:
Resultant force = Force of gravity - Lift force
Resultant force = 2.50 lb - 4.65 lb
Resultant force ≈ -2.15 lb
The negative sign indicates that the resultant force is directed downwards.
4. Calculate the angle of inclination:
To determine the angle of inclination, we can use the trigonometric relationship between the gravitational force, lift force, and the angle:
tan(θ) = Lift force / Force of gravity
Substituting the given values:
tan(θ) = 4.65 lb / 2.50 lb
θ ≈ arctan(1.86)
θ ≈ 62.83°
So, the angle of inclination is approximately 62.83 degrees.
5. Calculate the wind force acting on the kite:
The wind force acting on the kite can be calculated using the formula F = 0.625 * A * V^2, where F is the wind force, A is the area of the kite, and V is the wind speed.
Given that the area of the kite is 8 square-ft and the wind speed is 20 mph, we can substitute these values into the formula:
F = 0.625 * 8 sq-ft * (20 mph)^2
F ≈ 200 lb
So, the wind force acting on the kite is approximately 200 lb.
6. Determine the net force on the kite:
The net force on the kite is the vector sum of the wind force and the resultant force. Since the forces act in different directions, we subtract the resultant force from the wind force:
Net force = Wind force - Resultant force
Net force = 200 lb - (-2.15 lb)
Net force ≈ 202.15 lb
Therefore, the net force on the kite is approximately 202.15 lb.
Note: This explanation assumes a flat plate model for the kite and doesn't consider other factors like air resistance or the specific design of the kite.