Understanding Gravity: The Role of Forces in Momentum Questions

[404]

I was doing some momentum questions. There some that goes like "a man dives into water, and comes to a stop x seconds after reaching water, what force did the water act on him" or "stuntman jumps onto a mattress, matress compressed down x meters before he is brought to rest, what force did the matress apply on him?"
Basically, answer= (guys mass)(acc. of medium) + 9.8(guys mass)

Everytime I do those questions, I keep forgetting account for gravity, and I don't know why you are suppose to add 9.8*(guys mass). I mean, isn't gravity pulling the guy down, while the water/mattress's force is pushing the guy upwards, to stop him? So why do you add the 2 forces, if anything, wouldn't you subtract? (someone please clear this up for me )

 

[quantumdude]

Sorry for the late reply. In case you're still interested, here are my comments on this.

I was doing some momentum questions. There some that goes like "a man dives into water, and comes to a stop x seconds after reaching water, what force did the water act on him" or "stuntman jumps onto a mattress, matress compressed down x meters before he is brought to rest, what force did the matress apply on him?"

Basically, answer= (guys mass)(acc. of medium) + 9.8(guys mass)

The matress supplies an upward force that has to do 2 things:

1.) Decelerate the man.
2.) Support his weight.

So if we apply Newton's second law to the man + mattress system we have:

$$\Sigma F=F_{mattress}-mg=ma$$

So you are subtracting the two forces. And as you can see, upon solving for $F{mattress}$ you get $mg+ma$.

 

[Physwiz]

here's another way of looking at it...

downward force= (mg+ma)...this is applied onto the surface by the guy

for every force applied to the surface(mattress/water)...there will be an equal and opposite reaction by the surface in the upward direction...