Gravitational potential energy question - normal force on us

[Vash25]

Hi,

If we are standing on the ground, the Earth applies a force equal to our weight to us, but why do we feel a greater force when we fall to the ground from a certain height? Our weight is the same along this small height because our mass and acceleration are the same and, even so, the normal force is greater.

Thanks

 

[kuruman]

To keep you at rest while you are at rest relative to the ground, the ground must exert a force mg on you directed up. To stop you from moving and cause you to be eventually at rest relative to the ground, the ground must exert a force greater than mg directed up. Once you come to rest, the force that the ground exerts is back to being mg up.

 

[Mister T]

Summary:: why do we feel a greater force when we fall to the ground from a certain height?

Our weight is the same along this small height because our mass and acceleration are the same and, even so, the normal force is greater.

No, your acceleration is not the same. When you're standing still your acceleration is zero. When you fall to the ground, you have an acceleration between the time that you first make contact with the ground and the time you come to a stop.

You may be under the misconception that when you are standing still the upward force equals $mg$, but that does not mean that your acceleration is $g$.

Your acceleration is $g$ when you're in free fall, but when you are standing still on the ground you are not in free fall.

 

[jbriggs444]

One way of thinking about it is that the average supporting force holding you up over time comes out to mg. If it were less, you'd wind up accelerating downward on average. It it were more, you'd wind up accelerating upward on average.

If you fall further, you take longer to fall. When you hit bottom, the ground has to make up that missing supporting force. The longer the interval of support force you miss while falling, the more extra support the ground has to make up when you smash down. [And you make a bigger hole in the ground and get more broken bones in your body]

 

[anorlunda]

If you remove gravity, it might be easier to understand.

Why does a bullet shot horizontally from a gun cause more damage than a bullet thrown by hand?
The answer has nothing to do with gravity.

 

[A.T.]

If we are standing on the ground, the Earth applies a force equal to our weight to us, but why do we feel a greater force when we fall to the ground from a certain height? Our weight is the same along this small height because our mass and acceleration are the same and, even so, the normal force is greater.

The acceleration relevant for the support force is the acceleration relative to free fall (proper acceleration that an accelerometer measures):

- If you are standing on the ground your proper acceleration is 1g upwards, hence the support on you from the ground is mg upwards.

- When reducing vertical downward speed your proper acceleration is more than 1g upwards, hence the support on you from the ground is more than mg upwards.

 

[Vash25]

No, your acceleration is not the same. When you're standing still your acceleration is zero. When you fall to the ground, you have an acceleration between the time that you first make contact with the ground and the time you come to a stop.

You may be under the misconception that when you are standing still the upward force equals $mg$, but that does not mean that your acceleration is $g$.

Your acceleration is $g$ when you're in free fall, but when you are standing still on the ground you are not in free fall.

Thank you Mr. T.

I have some doubts about your answer: I understand that the vertical net force when we are standing on the ground is zero, therefore our acceleration is also zero. Ok, in free fall our acceleration is "g". Imagine that we fall from two different heights, when we fall to the ground we feel a greater force under our feet when the height is greater, but the force that we exert on the ground must be the same "mg" for both heights, therefore the normal force on us should be "mg" regardless of height. I know something in my reasoning is wrong but I don't know what. Thanks

 

[Vash25]

To keep you at rest while you are at rest relative to the ground, the ground must exert a force mg on you directed up. To stop you from moving and cause you to be eventually at rest relative to the ground, the ground must exert a force greater than mg directed up. Once you come to rest, the force that the ground exerts is back to being mg up.

Thanks Mr. Kuruman,

I still have a doubt. Imagine that we fall from two different heights, when we fall to the ground we feel a greater force under our feet when the height is greater, but the force that we exert on the ground must be the same "mg" for both heights, therefore the normal force on us should be "mg" regardless of height. I know something in my reasoning is wrong but I don't know what. Thanks

 

[jbriggs444]

but the force that we exert on the ground must be the same "mg" for both heights, therefore the normal force on us should be "mg" regardless of height.

Newton's third law: The downward force of you on the ground is equal to the upward force of the ground on you.

Newton's second law: The net force on you is equal to your acceleration times your mass.

The net force on you is the vector sum of the upward force of the ground on your feet and the downward force of gravity on your whole body.

When you are in the process of landing on the ground, you are going from a state of falling down to a state of standing still. You are accelerating upward.

Put this all together. The upward force on you from the ground has to be enough more than the downward force of gravity to account for your upward acceleration. So naturally this upward force has to exceed mg. It follows that the downward force of you on the ground has to exceed mg.

If you fall farther then when you land, you either have to accelerate upward more strongly or accelerate upward for a longer interval or both.

 

[Dale]

the force that we exert on the ground must be the same "mg" for both heights

This is not correct. Can you explain your reasoning why you believe this?

 

[Mister T]

Imagine that we fall from two different heights, when we fall to the ground we feel a greater force under our feet when the height is greater, but the force that we exert on the ground must be the same "mg" for both heights, therefore the normal force on us should be "mg" regardless of height.

The force that your feet exert on the ground is equal in magnitude to the force that the ground exerts on your feet (Newton's Third Law).

The magnitude of these forces is greater when you fall from a greater height.

 

[A.T.]

Imagine that we fall from two different heights, when we fall to the ground we feel a greater force under our feet when the height is greater, but the force that we exert on the ground must be the same "mg" for both heights, therefore the normal force on us should be "mg" regardless of height.

The exact impact force depends on the acceleration of the center of mass during the impact, which depends on many factors, like deformation of the ground and of the object. Estimating this can get very complicated, especially for complex objects like humans, which can bend their joints to dampen the fall, and thus control the maximal impact force to a certain degree.

So impact force is not a fixed value for given fall height, but must be greater than mg for some time period.

I know something in my reasoning is wrong but I don't know what.

Yes, but you don't really present the reasoning, just its result, so we cannot point out the error in it more precisely.

Try drawing a free body diagram and applying Newton's Laws to it.

 

[Delta2]

You have additional momentum when you fall to the ground from a certain height (because your potential energy has been converted to kinetic energy). The force from the ground has to counter both your weight and the additional momentum. To be more precise it is the change (from having velocity $v=\sqrt{2gh}$ where h the height, you come to a full stop) in your momentum that requires the additional force.