# Force exerted on the ground by pushing, pulling and striking

## Main Question or Discussion Point

Hello there, I know this may seem basic physics but I would be interested in how to calculate various things concerning force output on the ground when I, a machine or an object pushes another.

A few examples, a machine, lets say a large digger sort of contraption is pushing 100 tons of metal to a construction site, how much force does it exert on the ground?

I am also curious, how would one calculate how much force would be required to damage the ground? lets say this vehicle is travelling over a perfectly smooth surface of granite or steel (does not matter) how would you calculate the force that surface can take before cracking, shattering etc?

Is it compressive strength, tensile strength or something else in materials?

Finally, the same question goes for a human or something of that shape (a humanoid machine like a big Asimo?) pushing a very large object like a metal cube weighing in the double to triple digit tons, I am interested in knowing how much force would be acting as pressure on the ground from it pushing this object along a flat surface.

Thank you for any answers or aid.

## Answers and Replies

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anorlunda
Mentor
Thanks for that, do you mind giving me a basic "framework" calc I may be able to use myself with my own variables?

Lets say an example where someone is pushing a brass cube along a straight smooth granite surface.

Lets say the cube being pushed weighs 1000 tons and is moved at about 2 m/s

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Nugatory
Mentor
Thanks for that, do you mind giving me a basic "framework" calc I may be able to use myself with my own variables?

Lets say an example where someone is pushing a brass cube along a straight smooth granite surface.

Lets say the cube being pushed weighs 1000 tons and is moved at about 2 m/s
- Use the coefficient of dynamic friction to calculate the frictional force that is trying to slow the block.
- Note that the block is moving a a constant speed so its acceleration is zero. Use $F=ma$ to calculate the net force on the block (zero, because $a$ is zero).
- Calculate the force that, added to the frictional force, results in a net force of zero. That's the force that the pusher is exerting on the block.

The same approach works with a few more steps to get the force the pusher is exerting on the earth.
- Use Newton's third law to calculate the force the that block is exerting on the person doing the pushing
- Use $F=ma$ to find the net force on the person (it will be zero).
- Calculate the force the earth must be exerting on the person's feet to make the net force come out to zero.
- Use Newton's third law to find the force exerted on the earth by the person's feet.

These problems are much easier if you draw a diagram in which all of the forces acting on each object, and their directions, are shown. These are sometimes call "free body diagrams" and Google will find you many examples. Also google for "Newton cart horse" and be sure that you completely understand that problem before you try taking on anything trickier.

Thank you Nugatory. so I had a go myself, i cheated a bit using this calculator;

https://www.easycalculation.com/physics/classical-physics/kinetic-friction.php

The example I gave myself this time was a person shoving 3 250 ton brass cubic blocks (they are stacked on top of each-other) from resting (atop a smooth, vertical dry brass surface) to moving away from him up to an almost instantaneous acceleration of 4 m/s , the numbers are large because I thought I would give myself some room to work with whole numbers before they became decimals after some divisions. In any case here is my math;

Normal force; 226796 kg (brass blocks) x 9.8 (gravity) = 2222600.8 N

Kinetic Friction coefficient; I used this source; http://www.tribology.fink.rs/journals/2012/2012-1/3.pdf

Which unless I read it wrong suggests Brass on brass is around 0.1 which I went with although it seems to change. This change I find difficulty with understanding alongside force and time.

Anyway I put my numbers in the fields of that calculator which gave me a 22679.6 N Kinetic friction force. Which i assume is the force applied to the brass floor?

Any aid or input on this attempt of mine would be appreciated, thank you.

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