Mass Free Fall

[jerryez]

A 10 kg mass is in free fall with no air resistance. In order to slow the mass at a rate equal to the magnitude of g, an upward force must be applied with magnitude:


F=ma



F=(10kg)(9.81m/s2) = approximately 100N

So in order to slow the mass at a rate equal to g it should be a force less than 100N?? Im not sure how to figure this out. Help!!!

Thanks

Jerry Zink

 

[rock.freak667]

Let's start with the forces on the body falling.

There are three forces acting or well two since we are ignoring air resistance. What are these two and what direction are they going in (up or down)?

Since the body is moving downwards, the resultant force, ma, is downward. Can you formulate an expression for the resultant force ma?

 

[jerryez]

The two forces are

1. gravitational force on the 10kg mass "going down"
2. The upward force "going up"

So the upward force must go against the force of gravity plus the force of the mass.

The mass has a force of F=ma = 100N downward

Since the upward force is in the opposite direction it has to counteract the downward force and slow it down to = g

Im just having trouble formulating the expression for the upward force.

 

[jerryez]

Would the upward force be :

F=m2a ?

F=(10kg)(2)(9.81m/s2) = 196N

is this correct?

 

[rock.freak667]

The two forces are

1. gravitational force on the 10kg mass "going down"
2. The upward force "going up"

Correct.

So the upward force must go against the force of gravity plus the force of the mass.

Right but remember, the force of gravity is the 'force of the mass'.

So you will have one going down and one going up (don't worry with the formulas for now, just use U for upwards and W for downward). If the mass is moving downwards, what direction should the resultant force be in?

 

[jerryez]

The resultant force should be in the upward direction

 

[rock.freak667]

The resultant force should be in the upward direction

The mass is falling in which direction?

 

[jerryez]

OH! So the resultant force is in the downward direction.

 

[rock.freak667]

OH! So the resultant force is in the downward direction.

Right so your resultant is

ma = W-U

and you identified the downward force as the force of gravity. So what is W equal to?

They want the resultant acceleration to be equal to g. So what is 'a'?

 

[jerryez]

so W = ma + u

a = 9.81m/s2

so W is equal to the downward force of 100N?

So this means u = W - ma

U = 100N - (10kg)(9.81m/s2)

U = 1.9N

Is this right?

Are you sure its not this "ma = U-W"

This would make more sense because then U is = to around 200N

 

[rock.freak667]

so W = ma + u

a = 9.81m/s2

so W is equal to the downward force of 100N?

So this means u = W - ma

U = 100N - (10kg)(9.81m/s2)

U = 1.9N

Is this right?

Are you sure its not this "ma = U-W"

This would make more sense because then U is = to around 200N

If your upward force is greater then your object is moving upwards and not falling.

Normally what you have is

ma = W-U-F_{air resistance}

Sorry though, I interpreted one part wrong. They want the mass to fall at 'g' right? Which is essentially with the force of gravity, which is constant. Since it's acceleration is constant, the resultant force is ?

 

[jerryez]

Is the resultant force still the force of the mass 100N downwards?

 

[rock.freak667]

Is the resultant force still the force of the mass 100N downwards?

No, the resultant force is the resultant of W and U. Since the mass is not accelerating anymore, the resultant force is zero.

 

[jerryez]

?? So if the resultant force is zero how do we find the upward force?

 

[rock.freak667]

?? So if the resultant force is zero how do we find the upward force?

If we have ma=W-U and ma=0, then wouldn't W-U=0 ?

 

[jerryez]

So if the upward force is equal to the downward force W=U

Fw = (10kg)(9.81m/s2)

W = 100N
U = 100N

This doesnt seem right?

 

[rock.freak667]

So if the upward force is equal to the downward force W=U

Fw = (10kg)(9.81m/s2)

W = 100N
U = 100N

This doesnt seem right?

Why not?

 

[jerryez]

Then wouldn't that implicate that the mass is not moving?

 

[rock.freak667]

Then wouldn't that implicate that the mass is not moving?

Not in this case. The body is falling. Which means it is traveling at a constant velocity.

 

[jerryez]

That makes sense, but the answer in my book says the upward force is equal to 200N. This is what is throwing me off. Maybe the book is wrong.

I really appreciate your help rock.freak667

Can you make any sense of the 200N answer?

Thanks again

Jerry Zink

 

[vela]

The resultant force should be in the upward direction

This is correct.

The mass is falling in which direction?

The fact that the mass is moving downward only tells you that the velocity vector points down. It doesn't tell you anything about the direction of the acceleration vector.

For 1D motion, if the speed of the object is increasing, the acceleration points in the same direction as the velocity. If it's slowing down, the acceleration points in the direction opposite to the velocity.

 

[ehild]

The body is slowing down at a rate of g from its downward velocity. It means that the acceleration is opposite to the velocity. Therefore it should point upward as Vela has explained, and its magnitude is g. Jerryez was right, the resultant force should be in the upward direction.

ma=mg=F-mg

ehild

 

[jerryez]

So if

downward Force = mg = 100N

ma=mg=F-mg

(10kg)(9.81m/s2) = F - (10kg)(9.81m/s2)

F = (98.1)+(98.1)
F = approximately 200N

So the upward force is twice as great as the downward force this makes the downward mass fall at g? Can someone explain the theory behind this?

 

[ehild]

S

So the upward force is twice as great as the downward force this makes the downward mass fall at g? Can someone explain the theory behind this?

The upward force will make the falling body slow down at a rate of g till it loses all its downward velocity. After that, it will rise.

ehild

 

[vela]

So the upward force is twice as great as the downward force this makes the downward mass fall at g? Can someone explain the theory behind this?

You're not taking into account the direction of the acceleration. Let's use the usual convention of positive being the upward direction and negative being the downward direction. If only its weight mg acts on the mass, you get

ma = -mg ⇒ a = -g

The negative sign indicates the mass accelerates in the downward direction at a rate of 9.8 m/s². With the upward force F of magnitude F=2mg acting as well, you get

ma = F - mg = 2mg - mg = mg ⇒ a = +g

Again the mass is accelerating at a rate of 9.8 m/s², but this time it's accelerating in the upward direction.