Solving the Plane's Weight and Horizontal Accel.

[vivekfan]

Homework Statement

On takeoff, the combined action of the engines and wings exerts an 8000 N force on the plane, directed upward at an angle of 65 degrees above the horizontal. The plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction. What is the weight of the plane and what is its horizontal acceleration?

Homework Equations

F= ma
m= w/g

The Attempt at a Solution

I'm confused because I wrote out on a free body diagram the forces in the y-direction. I put gravity, the normal force, and the y component of the force that the engine. But then I got stuck because there is no mass. The answer is just the y component of the engine force. But I don't really understand why. Once, I know the weight, then finding the horizontal acceleration is easy.

 

[LowlyPion]

Homework Statement

On takeoff, the combined action of the engines and wings exerts an 8000 N force on the plane, directed upward at an angle of 65 degrees above the horizontal. The plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction. What is the weight of the plane and what is its horizontal acceleration?

Homework Equations

F= ma
m= w/g

The Attempt at a Solution

I'm confused because I wrote out on a free body diagram the forces in the y-direction. I put gravity, the normal force, and the y component of the force that the engine. But then I got stuck because there is no mass. The answer is just the y component of the engine force. But I don't really understand why. Once, I know the weight, then finding the horizontal acceleration is easy.

The vertical component must be the weight of the plane. At that angle what is the vertical component of the 8000N? That's your weight.

Now you have the mass and the horizontal force, so ...

 

[nlightner]

I would like to clarify that the weight of the plane is not equal to the y component of the engine force. Weight is a force that is always directed downwards towards the center of the Earth, while the force exerted by the engines is directed upwards at an angle. Therefore, these two forces cannot be directly compared.

To solve for the weight of the plane, we can use the equation F=ma, where F is the weight, m is the mass of the plane, and a is the acceleration due to gravity (9.8 m/s^2). Since the plane is rising with constant velocity in the vertical direction, we know that the net force in the y-direction is equal to 0. This means that the weight of the plane must be equal in magnitude to the y component of the engine force. We can use trigonometry to find this component, which is equal to 8000 N * sin(65 degrees) = 7226.7 N.

To find the horizontal acceleration, we can use the same equation F=ma, but this time we are looking at the forces in the x-direction. We know that the net force in the x-direction is equal to the force exerted by the engines, which is 8000 N * cos(65 degrees) = 3325.8 N. We also know that the mass of the plane can be calculated using the equation m=w/g, where w is the weight we just found and g is the acceleration due to gravity. Therefore, m= 7226.7 N / 9.8 m/s^2 = 737.3 kg. Finally, we can plug these values into the equation F=ma to solve for the acceleration, which is equal to 3325.8 N / 737.3 kg = 4.51 m/s^2.

In summary, the weight of the plane is approximately 7226.7 N and its horizontal acceleration is 4.51 m/s^2. It is important to note that these values may vary depending on the specific conditions of the plane and the takeoff.