Unbalanced force to find altitude of airplane

In summary, an airplane with a mass of 3,000 kg flying at a constant speed will have a lift force equal to its weight, which is 29400 N. When its horizontal speed increases and the lift force increases to 30 kN, the acceleration is 0.2 m/s/s according to Newton's Second Law. To determine the change in altitude when the airplane has an instantaneous upward velocity of 25 m/s, you will need to use the equation F=ma and consider the change in lift force due to the increase in horizontal speed. Avoid using projectile motion equations as they do not apply to an airplane in flight.
  • #1
a_r_part
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Homework Statement
An airplane with a mass of 3,000 kg flies horizontally at a constant speed. The airplane then increases its horizontal speed and the lift force produced by its wings increases to 30 kN, increasing the airplane’s altitude. How much has the airplane’s altitude increased by when it has an instantaneous upward velocity of 25 m/s?
Relevant Equations
F=ma
Since the airplane is flying at a constant speed, then the lift force equals the weight of the airplane. This means that the lift force prior to acceleration is the mass * gravity constant = 29400 N.

When the airplane increases horizontal speed, the lift force increases to 30 kN. This means, using Newton's Second Law, that the acceleration is 0.2 m/s/s.

This is where I get lost: the question asks about altitude given speed. The formulas for projectile motion come to mind, but I don't know how to set them up.

Could someone provide hints for me to arrive at the answer?
 
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  • #2
a_r_part said:
Homework Statement:: An airplane with a mass of 3,000 kg flies horizontally at a constant speed. The airplane then increases its horizontal speed and the lift force produced by its wings increases to 30 kN, increasing the airplane’s altitude. How much has the airplane’s altitude increased by when it has an instantaneous upward velocity of 25 m/s?
Relevant Equations:: F=ma

I haven't been able to find a solution.
Per forum rules, please post an attempt.
Hint : How much was the lift force before the plane's speed increased?
 
  • #3
a_r_part said:
Since the airplane is flying at a constant speed, the lift force before acceleration is zero.
That would make it not so much an "airplane" as a "hole in the ground". The question specifically states "flying horizontally".
 
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  • #5
a_r_part said:
This is where I get lost: the question asks about altitude given speed. The formulas for projectile motion come to mind, but I don't know how to set them up.
Stay away from the projectile motion equations. They apply to objects in free fall. An airplane in free fall is not a good thing, especially for its passengers.
 
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Related to Unbalanced force to find altitude of airplane

1. What is an unbalanced force?

An unbalanced force is a force that causes an object to accelerate or change its motion. It is the result of the net force acting on an object, which is the sum of all the forces acting on the object.

2. How does an unbalanced force affect the altitude of an airplane?

An unbalanced force can affect the altitude of an airplane by either causing it to ascend or descend. If the force is greater than the force of gravity, the airplane will ascend. If the force is less than the force of gravity, the airplane will descend.

3. How can unbalanced forces be calculated to determine the altitude of an airplane?

To calculate the unbalanced force on an airplane, you need to know the mass of the airplane, the force of gravity, and the other forces acting on the airplane (such as thrust and air resistance). Once you have these values, you can use the equation F = ma, where F is the unbalanced force, m is the mass, and a is the acceleration.

4. Can unbalanced forces cause an airplane to reach a constant altitude?

Yes, unbalanced forces can cause an airplane to reach a constant altitude. If the forces are balanced, meaning the net force is zero, the airplane will maintain a constant altitude. This is often the case during level flight when the thrust force is equal to the force of gravity.

5. How does the altitude of an airplane change when unbalanced forces act on it?

The altitude of an airplane will change when unbalanced forces act on it. If the unbalanced force is greater than the force of gravity, the airplane will ascend. If the unbalanced force is less than the force of gravity, the airplane will descend. The magnitude and direction of the unbalanced force will determine the rate and direction of the altitude change.

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