Homework Help: Mass Free Fall

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?

 

Correct.

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?

 

The mass is falling in which 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'?

 

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 ?

 

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

 

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

 

Why not?

 

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

 

This is correct.

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.

 

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

 

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

 

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.