A paraglider is flying horizontally at a constant speed. Assume that only two forces act on it in the vertical direction, its weight and a vertical lift force exerted on its wings by the air. The lift force has a magnitude of 1900 N. For both questions, take the upward direction to be the +y direction.
If the lift force should suddenly decrease to 1000 N, what would be the vertical acceleration of the glider
1900 N must be the weight, since it flies horizontally with that lift force. The mass must be 1900 N/g = 193.9 kg
The presumably includes the weight of the person flying the paraglider.
With a lift force of 1000 N, there is a net downward force of 900 N. The acceleration would be
F/m = 900 N/(1900 N/g) = (9/19)*g
= 4.64 m/s^2
To determine the vertical acceleration of the glider when the lift force suddenly decreases to 1000 N, we need to calculate the net force acting on the glider in the vertical direction.
Given:
Lift force (initial) = 1900 N
Lift force (final) = 1000 N
Step 1: Determine the force of gravity acting on the glider.
The force of gravity or weight (W) acting on the glider is equal to its mass (m) multiplied by the acceleration due to gravity (g). Since the glider is flying horizontally at a constant speed, the vertical acceleration is zero. Therefore, the weight of the glider is given by W = m * g, where g ≈ 9.8 m/s^2.
Step 2: Calculate the net force.
To find the net force in the vertical direction, subtract the lift force (final) from the force of gravity.
Net force (F_net) = Weight - Lift force (final) = m * g - 1000 N
Since we don't have the mass of the glider, we cannot determine the exact value of the net force or the vertical acceleration.
However, if the net force is positive (F_net > 0), the glider will experience an upward acceleration, and if it is negative (F_net < 0), the glider will experience a downward acceleration.
To determine the vertical acceleration of the glider when the lift force decreases from 1900 N to 1000 N, we need to calculate the net vertical force acting on the glider.
Given:
Lift force after decrease = 1000 N
Weight force = mg, where m is the mass of the glider and g is the acceleration due to gravity (approximately 9.8 m/s²)
Initially, when the lift force was 1900 N, the net vertical force was the difference between the upward lift force and the downward weight force:
Net Force = Lift Force - Weight Force
= 1900 N - (mg)
When the lift force decreases to 1000 N, the new net vertical force will be:
Net Force = 1000 N - (mg)
Now, we can relate the net force to the vertical acceleration using Newton's second law:
Net Force = ma
Therefore,
ma = 1000 N - (mg)
To find the vertical acceleration (a), we need to rearrange the equation, dividing both sides by the mass (m):
a = (1000 N - (mg)) / m
Hence, the vertical acceleration of the glider can be determined by dividing the difference between the new lift force and the weight force by the mass of the glider.