# Solving the Plane's Weight and Horizontal Accel.

• vivekfan
In summary, the plane experiences a combined upward force of 8000 N from the engines and wings, resulting in constant vertical velocity and horizontal acceleration. The weight of the plane can be found by calculating the vertical component of the force at the given angle, and using the weight and horizontal force, the horizontal acceleration can be determined using the equation F=ma.
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?

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.

vivekfan said:

## 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?

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 ...

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.

## 1. What is the equation for solving the plane's weight and horizontal acceleration?

The equation for solving the plane's weight and horizontal acceleration is Force = Mass x Acceleration, or F = ma. This equation is derived from Newton's second law of motion.

## 2. How do you determine the mass of the plane?

The mass of the plane can be determined by using a scale or balance to measure its weight. The weight is then divided by the acceleration due to gravity (9.8 m/s^2) to get the mass in kilograms.

## 3. Why is it important to solve for the plane's weight and horizontal acceleration?

Knowing the weight and horizontal acceleration of a plane is important for various reasons, including calculating its fuel consumption, determining its takeoff and landing speeds, and ensuring it stays within safe weight limits.

## 4. What factors can affect the plane's weight and horizontal acceleration?

The main factors that can affect the plane's weight and horizontal acceleration include the weight and distribution of passengers, cargo, and fuel, as well as external forces such as wind and air resistance.

## 5. How can solving for the plane's weight and horizontal acceleration help with flight safety?

By accurately determining the plane's weight and horizontal acceleration, pilots and aviation engineers can ensure that the plane stays within its safe operating limits and avoid potential accidents due to overloading or improper weight distribution.

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