# Why is it that despite there being a higher force, objects sometimes don't accelerate as much?

Consider the following situations.

A truck moving at 0.5m/s hits you. Said truck is around 2000KG. This truck must surely exert a great force, but if you get hit by it before the brake is quickly pressed, you barely might get pushed back a bit (or just feel something pushing you).

Or consider a hydraulic press (which would multiply the force it's given to compress something), which slowly compresses objects, but if your hand happens to just touch it while it's going down, your hand won't move much. Sure, you might not be able to resist or stop it, but at the moment of contact your hand just slowly gets pushed down. If you happen to get stuck, your hand won't be in a good shape afterwards, but the acceleration your hand receives is very low.

But someone pushing you with their hand can move you much more than those, even though the force is technically much lower.

So how does this all exactly work? How does A=F/M exactly apply?

Edit: The fundamental problem I think here is that the moment you accelerate, you end up moving as fast (or faster) as whatever is pushing you, reducing the force on you until you slow down again. Now for that, you can argue that, so Newton's law would still apply but then there is the concept of objects compressing and bouncing back with even greater velocity (this is more noticeable with something like a ball being hit) which makes things even more complicated in regards to how force and acceleration work.

So how is this all supposed to work? Was Newton only half-right or what?

• I don't think you have a proper mental image of being hit by a 2000kg truck moving at 0.5m/s. Also, how do you expect your hand to move faster than the press is moving? If your hand speed gets too high you lose contact with the press and no more force is exerted. Like a car with infinite torque won't continue to accelerate to infinite speed if the wheels themselves can't spin at infinite speed. Commented Jan 30, 2022 at 5:16
• In the reference frame of the truck / press your body / hand is moving towards it with a minuscule velocity. Upon collision (if we neglect the dissipation of energy) it gets bounced back with equal speed and opposite direction. From the rest reference frame this corresponds to twice the speed of truck / press. So it is the speed of the truck that determines the speed at which you will be pushed away from it, not the force Commented Jan 30, 2022 at 5:19
• That's what I was thinking, but in that case, won't that apply to any object collision? And so when would you even use A=F/M? The fundamental problem I think here is that the moment you accelerate, you end up moving as fast as whatever is pushing you, reducing the force on you until you slow down again. Commented Jan 30, 2022 at 5:24
• Then there is the concept of objects compressing and bouncing back with even greater velocity (this is more noticeable with something like a ball being hit) which makes things even more complicated in regards to how force and acceleration work. Commented Jan 30, 2022 at 5:31
• It's not clear what your question is. "The fundamental problem I think here is that the moment you accelerate, you end up moving as fast as whatever is pushing you, reducing the force on you until you slow down again." What you say is not true. Moving with the same acceleration as an object applying a force to you does not decrease the force on you.
– d_b
Commented Jan 30, 2022 at 8:58

Newton's laws are right, not half right, and if ever you think you have found an exception to them, you should assume you have failed to interpret and apply them correctly.

Bear in mind that a force will accelerate a mass in accordance with Newton's second law if and only if the force is applied to the mass. If a huge force is delivered at low speed to a small mass, the mass will quickly accelerate to the point at which its speed equals that of the source of the force. At that point the force is no longer in full contact with the mass and so the acceleration stops.

You should also bear in mind that all kinds of transient effects come into play which are easily forgotten about. For example, if you were unfortunate enough to be hit by a truck, your body does not instantaneously accelerate as a unit- instead whichever part of your body first makes contact with the truck begins to accelerate, and it takes a finite time before a compression wave passes through your body and starts to accelerate the rest of it.

If you have a hydraulic press that is capable of exerting a force of 1,000,000 tonnes, but which moves at only one millimetre per second, you can place your hand against it and your hand will be irresistibly propelled at one millimetre per second. Your hand will not be rapidly accelerated to a huge speed because the full force the press is capable of generating will never be applied to your hand as a unit. Your hand will compress somewhat on first contact with the press and be accelerated to 1mm/s at which point the press can no longer apply the force because your hand is moving as fast as the press is.

Newton's second law is an "instantaneous" equation. What I mean by this is that $$F_\text{net}=ma$$ relates the net force and acceleration of a mass at the same instant in time.$$^*$$ It seems like (one of) your confusion is arising mostly because you are considering the force at one time and the acceleration at another. This is specifically in the case of an object moving due to a force which then changes the force that is being applied to the object.

Specifically about the hydraulic press... I think you misunderstand when the large force "happens". As it is moving down before it is in contact with anything is not exerting a force on anything, and if you were to touch it out would not be exerting a force on you equal to the force it exerts while it is crushing something. The crushing force relies on the contact with the object and bottom surface as the machine pushes down harder and harder. You can even experience this yourself by moving your hand slowly down to the table and then pushing down harder and harder into the surface of the table.

$$^*$$With extended, non-rigid bodies you have to be a little more careful with something like this, but it still applies at the "point mass" level regardless.