Force exerted at given angle, constant velocty, find weight

In summary, the plane is experiencing an upward force of 7546 N at an angle of 70.5 degrees above the horizontal. It is rising with constant velocity in the vertical direction and accelerating in the horizontal direction. Using Newton's law, the sum of the forces in the y direction is Fsin70.5 - w = ma, where w is the weight of the plane and a is the acceleration in the y direction. Since the plane is rising with constant velocity, a is equal to 0 and the equation becomes Fsin70.5 = w. Thus, the weight of the plane is equal to the vertical component of the exerted force, which is 7546N * sin70.5 = 7338.
  • #1
AR8742
3
0

Homework Statement


On takeoff, the action of the air around the engine and wings of an airplane exerts a 7546 N force on the plane, directed upward at an angle of 70.5 degrees above the horizontal. The plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction. Acceleration due to gravity is 9.8m/s^2. What is the weight of the plane (in N)?


Homework Equations


I think I should use F=ma. (?)


The Attempt at a Solution


My first problem is I'm not quite sure if I have the free body diagram right. I have the plane's weight in the downward direction, normal force in the upward direction, and the (7546 N) force in between the normal force and the horizontal axis at 70.5 degrees. It's hard to know if I'm on the right track if that isn't right. From there I simply tried m=F/a. m = 7546N / 9.8m/s^2 = 770 kg? That would be too easy though and I feel like a calculation for acceleration is necessary? My previous problems involved finding acceleration with friction forces so I am a bit thrown off by this for some reason. Do I have to find the sum of the forces? Just looking if someone can point me in the right direction either with the free body diagram or an equation. Thanks!
 
Physics news on Phys.org
  • #2
AR8742 said:

Homework Statement


On takeoff, the action of the air around the engine and wings of an airplane exerts a 7546 N force on the plane, directed upward at an angle of 70.5 degrees above the horizontal. The plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction. Acceleration due to gravity is 9.8m/s^2. What is the weight of the plane (in N)?


Homework Equations


I think I should use F=ma. (?)


The Attempt at a Solution


My first problem is I'm not quite sure if I have the free body diagram right. I have the plane's weight in the downward direction, normal force in the upward direction, and the (7546 N) force in between the normal force and the horizontal axis at 70.5 degrees.

Since they say the plane is rising, it has already left the ground, so one of these forces should is not present.

It's hard to know if I'm on the right track if that isn't right. From there I simply tried m=F/a. m = 7546N / 9.8m/s^2 = 770 kg?

I think you need to be a bit more careful with Newton's law here. If you pick some specific direction (and call it the x direction), then it is:

[tex]
\sum F_x = m a_x
[/tex]

that is, add up all of the x components of the forces acting on the object, and then that's equal to mass times the x component of the acceleration.

So what is the best direction to apply Newton's law here, based on what they are asking? What do you get?
 
  • #3
Ok, that's what I was thinking...except I just wasn't sure I had all of the forces right in my free body diagram. So there would be no normal force then (just weight and the exerted force)? If I make the +x direction on the horizontal axis my sum would be Fcos70.5 = (ma) in x direction and my sum in the +y direction would be Fsin70.5-w =(ma)in y direction. But at this point I am still confused because I don't know the plane's weight or acceleration. I'm sure this problem isn't that difficult but for some reason nothing is clicking for me about where to go from here.
 
  • #4
AR8742 said:
Ok, that's what I was thinking...except I just wasn't sure I had all of the forces right in my free body diagram. So there would be no normal force then (just weight and the exerted force)? If I make the +x direction on the horizontal axis my sum would be Fcos70.5 = (ma) in x direction and my sum in the +y direction would be Fsin70.5-w =(ma)in y direction. But at this point I am still confused because I don't know the plane's weight or acceleration. I'm sure this problem isn't that difficult but for some reason nothing is clicking for me about where to go from here.

You're trying to find the planes weight, so the y-equation is the one to use. What is the acceleration in the y direction?
 
  • #5
Is it 9.8m/s^2?
 
  • #6
AR8742 said:
Is it 9.8m/s^2?

No, but you can determine the vertical acceleration from the fact that it says the plane rises with constant velocity in the vertical direction. What would that be?
 

1. What is force exerted at a given angle?

Force exerted at a given angle refers to the amount of force applied to an object at a specific angle from the horizontal. It is measured in newtons (N) and is the product of the mass of the object and its acceleration due to gravity.

2. How do I calculate the force exerted at a given angle?

To calculate the force exerted at a given angle, you can use the formula F = mg sinθ, where F is the force exerted, m is the mass of the object, g is the acceleration due to gravity (usually 9.8 m/s²), and θ is the angle at which the force is applied.

3. What does constant velocity mean?

Constant velocity refers to the motion of an object at a steady speed in a straight line. This means that the object is not accelerating or decelerating, and its displacement over time is consistent.

4. How does constant velocity affect the force exerted?

When an object is moving at a constant velocity, the force exerted on it is balanced by the opposing forces acting on it. This means that the net force is equal to zero, and there is no change in the object's motion.

5. How do I find the weight of an object using force exerted at a given angle and constant velocity?

To find the weight of an object in this scenario, you can use the formula W = F cosθ, where W is the weight of the object, F is the force exerted at the given angle, and θ is the angle at which the force is applied. This is because weight is a component of the force acting on the object in the vertical direction.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
1K
Replies
6
Views
683
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
2K
Replies
22
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
445
  • Introductory Physics Homework Help
2
Replies
41
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
1K
  • Introductory Physics Homework Help
Replies
20
Views
1K
Back
Top