# Question about Force (I think)

There's something that has been bothering me since we started learning about Force in physics class. The general equation for force, F=ma just doesn't seem right. I understand the equation and don't have any problem figuring out problems or anything. I can even sort of visualize what force is in my head for most problems.

But there is a specific circumstance that I don't understand it. This is the easiest example I can come up with:

Lets say you are standing on a trampoline. The trampoline will go down a bit from the force of you standing on it (ie, your mass * 9.8)

But, if you start jumping on it, the trampoline will go down further than it did when you were only standing. Logically speaking (well, my logic) it takes a greater force to push the trampoline down further. However, according to F=ma, your force is still your mass * 9.8 (the same as when you were standing)

So it seems to me that force should somehow directly incorporate velocity. I've talked to my physics teacher and he didn't really have an answer, but one thing he did tell me is the equation for momentum, p=mv, so F=p/t, so F=mv/t. But that doesn't help any because the velocity still gets divided by time, so it doesn't really have a direct influence on the force.

I'm guessing there is some concept I just probably haven't learned yet, but this is really bugging me. Any help?

When standing, the trampoline springs deflect in accordance with F = ky. The "k" is the spring constant, & y is vertical displacement.

When jumping, the trampoline springs deflect an additional amount because you now have vertical kinetic energy established. If the vertical velocity is "vy", then KE = 0.5*m*vy^2. This KE will be transferred into spring energy 0.5*k*y^2. Your weight, mg, will also produce spring displacement.

The 2 components sum to a total greater than just 1 component when you were standing.

Did I help?

Sorry for the double post, but I think it just dawned on me what the answer is:

The force applied by the trampoline changes the acceleration of the object (so that it is now slowing down.) But that doesn't mean that the object changes direction of the velocity at that point. Instead the velocity decreases until it changes direction, and starts going backward. In the time that it takes for the velocity to change direction, the object is STILL moving toward the trampoline (and thus pushing the trampoline further down)

That's the best I can explain it, but I think I'm on the right track?

(BTW, sorry for even asking the question lol I literally just had an 'oh yea' moment a couple minutes after I posted.)

EDIT: Thanks cabraham, I don't think you quite answered the question, but you did help me understand the situation better. I think where I was going wrong was I was just forgetting what I explained above.

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Many think that F=ma is the equation of force, but it is actually F=(change in momentum)/time, when you jump, your muscles do force in order to get you high, then when you fall you have that same energy in the form of kinetic energy. The time it takes your body to come to a stop is inversely proportional to the force exerted. That is why if you fall to a pillow it doesnt hurt, because the pillow 'delays' the stop, but when you fall to the ground its basically a sudden stop, so much more force is done.

Doc Al
Mentor
Lets say you are standing on a trampoline. The trampoline will go down a bit from the force of you standing on it (ie, your mass * 9.8)
If you are standing in equilibrium on the trampoline, then yes, the force you exert on the trampoline happens to equal your weight. But in general, the force you exert on the trampoline does not equal your weight.

But, if you start jumping on it, the trampoline will go down further than it did when you were only standing. Logically speaking (well, my logic) it takes a greater force to push the trampoline down further.
Right.
However, according to F=ma, your force is still your mass * 9.8 (the same as when you were standing)
That's your weight, not the force you exert on the trampoline.

Also realize that Newton's 2nd law states that the net force on you equals your mass * acceleration. There are two forces acting on you: your weight and the upward force from the trampoline (which does not generally equal your weight).

Sorry for the double post, but I think it just dawned on me what the answer is:

The force applied by the trampoline changes the acceleration of the object (so that it is now slowing down.) But that doesn't mean that the object changes direction of the velocity at that point. Instead the velocity decreases until it changes direction, and starts going backward. In the time that it takes for the velocity to change direction, the object is STILL moving toward the trampoline (and thus pushing the trampoline further down)
Sounds good to me. The trampoline 'wants' to stop you, but can only exert so much force. As you stretch the trampoline further, its force on you increases. Soon the trampoline is pushing up on you with a force greater than your weight, so you start accelerating upwards (since the net force on you is up). Your downward velocity slows and eventually you come to a stop--momentarily--then start moving upward.

A good refresher on the Newton's laws of motion and conservation laws will be good for you.

I teach calculus physics at a local university. I can't type equations here; it involves differentiation, vectors, etc. I will locate my file later and when I reply next time I will attach it. But a short answer:

Energy of a system is always conserved. Here the system is the jumper, trampoline, and the earth. The jumper, as he is about to hit the trapoline, has a given KE = (1/2)*mass*(velocity)**2. The trampoline has no KE. As the jumper hits the trampoline, he transfers his KE to trampoline, which stretches like a spring, and KE is now stored as PE. This PE is transferred back to the jumper as KE.

Nweton's laws, as they teach, are simple, but, actually, they are very complicated.
Talk to you later.

Please correct me if I am wrong on any of my points

Many think that F=ma is the equation of force, but it is actually F=(change in momentum)/time, when you jump, your muscles do force in order to get you high, then when you fall you have that same energy in the form of kinetic energy. The time it takes your body to come to a stop is inversely proportional to the force exerted. That is why if you fall to a pillow it doesnt hurt, because the pillow 'delays' the stop, but when you fall to the ground its basically a sudden stop, so much more force is done.

From what I understand both are correct (F=ma and F=p/t)

Change in momentum, using the formula p=mv, would require a change in velocity since the mass doesn't change (though, I remember reading somewhere that technically mass changes with speed, but it is so minute that we don't take it into account for general physics.) And changing the velocity is the same as acceleration, so p/t=m(delta v)/t=ma

Doc Al said:
If you are standing in equilibrium on the trampoline, then yes, the force you exert on the trampoline happens to equal your weight. But in general, the force you exert on the trampoline does not equal your weight.

Could you explain this? I don't understand what other forces would come into play other than the weight of the object (I am assuming if the object is a person, he doesn't move any of his muscles, etc.) To make it clearer, say the object is a bowling ball. Does that still exert some other force on the trampoline other than it's weight?

Doc Al said:
However, according to F=ma, your force is still your mass * 9.8 (the same as when you were standing)

That's your weight, not the force you exert on the trampoline.

Also realize that Newton's 2nd law states that the net force on you equals your mass * acceleration. There are two forces acting on you: your weight and the upward force from the trampoline (which does not generally equal your weight).

I do not see how your weight isn't the force you exert on the trampoline (again, assuming I'm not actively exerting force through my muscles). From my understanding, you are correct about the net force = ma (in fact, in class we are to write F(net)=ma, net being a subscript)

But still, the only force you are exerting on the trampoline is your weight. Of course the trampoline exerts force on you as well, which increases as you go further down (referencing another post) At some point, when the trampoline's force is greater than the force of your weight, your velocity will start decreasing. However, still having a downward velocity, you will continue to go downwards, which increases the trampoline's force on you, which accelerates you up faster, etc (a big cycle) until you reach a velocity of 0, at which point you finally start going up. The entire time however, you are exerting the force of your weight on the trampoline, just that the trampoline is exerting more force on you, so it wins and pushes you back up.

I might try to pick some numbers and figure things out mathematically using the equations I now know, but being that it's a Friday afternoon I would rather relax and think than actually do calculations.

Doc Al
Mentor
Could you explain this? I don't understand what other forces would come into play other than the weight of the object (I am assuming if the object is a person, he doesn't move any of his muscles, etc.) To make it clearer, say the object is a bowling ball. Does that still exert some other force on the trampoline other than it's weight?
Realize that the bowling ball's weight is a force that acts on the bowling ball, not on the trampoline. The force that the ball exerts on the trampoline is a contact force which has nothing directly to do with the ball's weight. Only in special circumstances will the force of ball on trampoline happen to equal the weight of the ball.

Try this. Rest a bowling ball on your foot. The force it exerts is equal to its weight. Now drop the ball from a height of three feet onto your foot. Do you still think that the force the ball exerts on your foot is the same and always equal to its weight?

But still, the only force you are exerting on the trampoline is your weight. Of course the trampoline exerts force on you as well, which increases as you go further down (referencing another post)
Don't forget Newton's 3rd law: Whatever force the trampoline exerts on you must be equal and opposite to the force that you exert on the trampoline.

K^2