WEIGHT and ACCELERATION as you FALL and CLIMB UP

In summary: You could think of it as your weight is being added to the force of gravity. (In this case, the acceleration of the frame of reference is downwards, so the opposite is true.)In summary, the apparent weight during free-fall is zero, and the acceleration of the plane must be 3.92m/s^2 in order for the apparent weight to be 60% of the true weight. When the plane climbs back up with an equal and opposite acceleration, the apparent weight will be 140% of the true weight.
  • #1
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1. An airplane flying horizontally encounters a low pressure and drops, and you feel lighter. If your apparent weight during that time is 60% of your true weight, what is the acceleration of fall of the plane? If the plane now climbs back with an acceleration equal and opposite to the acceleration of fall, what will be your apparent weight at that time?



2. ? Net Force = mass x acceleration ? Weight = (-)mass x acceleration of free fall of 9.8 ?



3. ??Not sure how to start this. I was thinking maybe the acceleration of the fall of the plane would be acceleration of free fall -g = -9.8. But there is no way that it could be this easy. There is a vital piece of information I am missing out on! And if -9.8 is the acceleration of the fall, then 9.8 would be acceleration of it climbing back up. So if i did use the weight = mass x acceleration equation. Apparent weight would be 140% of true weight??

I'm very confused, so any assistance will be very much appreciated!
 
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  • #2
Welcome to PF!

sousou_88 said:
1. An airplane flying horizontally encounters a low pressure and drops, and you feel lighter. If your apparent weight during that time is 60% of your true weight, what is the acceleration of fall of the plane? If the plane now climbs back with an acceleration equal and opposite to the acceleration of fall, what will be your apparent weight at that time?

There is a vital piece of information I am missing out on!

Hi sousou_88! Welcome to PF! :smile:

The vital piece of information you are missing is R, the reaction force on you (from the airplane) …

good ol' https://www.physicsforums.com/library.php?do=view_item&itemid=26" won't work without it. :wink:

(and R is also your apparent weight)
 
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  • #3
Answer# 1. as we know that the equation relating the Apparent and the Real weight is given as
Fnet=W(real)-W(apparent)...1

but
W(real)=Mg..........2
W(app)=60% X W(real).......3
and F(net)=Ma.........4
where M is the mass of the aeroplane

so Ma =Mg-0.60xMg

this gives us that "a" is = gx(0.40) = 3.92m/s^2

this is the acceleration with which the aeroplane must fall...
 
  • #4
A good way to approach this problem would be with fictitious forces. A free body diagram from the accelerated point of view, would reveal three forces acting on you, one of them is the fictitious force, and the other two are the force of gravity, and the reaction force from the airplane. From the accelerated frame, you are at rest.

For a positive y-axis pointing down, the direction of the acceleration is also down, and positive. Remember that the fictitious force is opposite the direction of the acceleration of the frame of reference.

Fd = -mA
Fg = mg
The reaction force is your apparent weight (Negative sign, as it is pointing up)

I think that a point that's confusing you is what your weight during free-fall would be. In free-fall, you are weightless!
Gravity has an equal effect on everything around you, you are not accelerating relative to the scale you're standing on, so you don't enact any force on it.
If you were being accelerated at a constant acceleration g, upwards, your apparent weight would be twice your actual weight.
 
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1. How does weight affect acceleration when falling?

Weight does not affect acceleration when falling. According to the law of universal gravitation, all objects fall at the same rate regardless of their weight. This means that a feather and a brick will fall at the same rate in a vacuum, even though the brick is much heavier.

2. Why do we feel heavier when going down in an elevator?

When going down in an elevator, we feel heavier because the elevator is accelerating downwards. This acceleration creates a force on our bodies, making us feel heavier. However, our actual weight does not change, as weight is a measure of the force of gravity on an object.

3. Does acceleration affect weight?

No, acceleration does not affect weight. Weight is a measure of the force of gravity on an object, while acceleration is the rate of change of an object's velocity. While weight can affect acceleration (such as in the case of falling objects), acceleration itself does not affect weight.

4. How does weight affect acceleration when climbing up?

Weight does not affect acceleration when climbing up. Again, according to the law of universal gravitation, all objects fall at the same rate regardless of their weight. This means that when climbing up, an object's weight will not change the rate at which it accelerates.

5. How does air resistance affect acceleration when falling?

Air resistance can affect the acceleration of a falling object. As the object falls, it will experience a force from the air pushing against it, known as air resistance. This force increases as the object's velocity increases, eventually reaching a point where it is equal to the force of gravity. At this point, the object will reach a terminal velocity and stop accelerating.

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