Perpendicular Forces Homework: Solving for mg/cos20

In summary: In which direction can you be sure there is no acceleration? For that direction, you know that the sum of forces is zero. What is the component of lift in that direction?The component of lift in the vertical direction is weight (mg).
  • #1
ravsterphysics
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Homework Equations

The Attempt at a Solution


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I was of the understanding that the slope can be calculated as mgsin20 whereas the force acting straight down through the lift is mgcos20 but the answer is mg divided by cos 20??
 
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  • #2
Hint: What force components act in the vertical direction? What must they add to?
 
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  • #3
Doc Al said:
Hint: What force components act in the vertical direction? What must they add to?

in the vertical direction we have weight acting downwards and lift acting upwards? so does it look like this?
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  • #4
ravsterphysics said:
in the vertical direction we have weight acting downwards and lift acting upwards?
The weight acts downward. Good! But only a component of the lift force acts vertically. What is that component?
 
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  • #5
Doc Al said:
The weight acts downward. Good! But only a component of the lift force acts vertically. What is that component?

So only the 'top' part of the weight is what we're after? And the angle is also 20 degrees? So it looks like this?

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in which case lift would then be Lift = mg/cos20

I see!

In that case, how does this differ to my notes that say the perpendicular force to the slope would be mgcos20? Is it because we're dealing with a component only?
 
  • #6
ravsterphysics said:
So only the 'top' part of the weight is what we're after?
Not sure what you mean. There are two forces acting on the wing: Weight, which acts down. And the lift force, which acts at the angle shown.

You need to analyze the vertical components.

ravsterphysics said:
And the angle is also 20 degrees?
The angle that the lift force makes with the vertical is 20 degrees. So what is the vertical component of that force?
 
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  • #7
Doc Al said:
Not sure what you mean. There are two forces acting on the wing: Weight, which acts down. And the lift force, which acts at the angle shown.

You need to analyze the vertical components.The angle that the lift force makes with the vertical is 20 degrees. So what is the vertical component of that force?

The vertical component is weight (mg) right? So to get lift, we use trig to end up with Lift = mg/cos20? Is that what you mean by vertical component?

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  • #8
ravsterphysics said:
The vertical component is weight (mg) right? So to get lift, we use trig to end up with Lift = mg/cos20? Is that what you mean by vertical component?
No. I simply mean: What is the component of the lift force in the vertical direction? You know the angle to the vertical, so how would you find the vertical component? (It will be in terms of L. You'll then use it to solve for L.)
 
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  • #9
Doc Al said:
No. I simply mean: What is the component of the lift force in the vertical direction? You know the angle to the vertical, so how would you find the vertical component? (It will be in terms of L. You'll then use it to solve for L.)

okay now I'm lost, i thought the mg/cos20 IS the vertical component? if not, can you write it, it'll probably click for me that way.
 
  • #10
I hope I'm not adding to your confusion!

ravsterphysics said:
i thought the mg/cos20 IS the vertical component?
Not quite.

ravsterphysics said:
in which case lift would then be Lift = mg/cos20
You had this correct! (Didn't see it earlier.)

But to be clear, here's how to figure out what L is.
(1) vertical component of L = L cos20 (This is what I was trying to get you to say!)
(2) vertical component of weight is just mg (of course, since it's vertical)

ΣFy = 0
L cos20 - mg = 0

Thus:
L cos20 = mg
L = mg/cos20

Does that make sense?
 
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  • #11
ravsterphysics said:
okay now I'm lost, i thought the mg/cos20 IS the vertical component? if not, can you write it, it'll probably click for me that way.
You should start by considering accelerations. You are told the direction of flight is (continuing) horizontal. So in which direction can you be sure there is no acceleration? For that direction, you know that the sum of forces is zero. What is the component of lift in that direction?
 
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FAQ: Perpendicular Forces Homework: Solving for mg/cos20

1. What is the formula for calculating perpendicular forces?

The formula for calculating perpendicular forces is F = mg/cosθ, where F is the perpendicular force, m is the mass, g is the acceleration due to gravity, and θ is the angle of the force with respect to the horizontal.

2. What is the significance of cos20 in the formula?

Cos20 represents the cosine of the angle at which the force is acting with respect to the horizontal. It is important to use the cosine function in the formula to account for the component of the force acting perpendicular to the surface.

3. How do I determine the value for mg in the formula?

The value for mg can be determined by multiplying the mass of the object in kilograms by the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth.

4. Can this formula be used for any angle of force?

Yes, this formula can be used for any angle of force as long as the angle is measured with respect to the horizontal. However, it is important to use the cosine function to accurately calculate the perpendicular force component.

5. How do I solve for the perpendicular force in this equation?

To solve for the perpendicular force, plug in the known values for mass, acceleration due to gravity, and angle in the formula F = mg/cosθ. Then, use basic algebraic operations to isolate the perpendicular force (F) on one side of the equation.

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