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# How do you find the force with which something hits the ground if you know the distance and weight?

Updated: 9/14/2023

Wiki User

15y ago

You can start by finding the change in energy of the object, which should be the work done on the object in the gravitational field: Int_(d0)^(d1) [F_g(r)] dr. If you're close enough to the surface of the Earth for the force of gravity to be the constant m*g, also known as the weight of the object, you can then get the simple equation (change in Energy) = dE = Wd where W is the weight of the object and d is the distance the object fell. This is also assuming negligible friction due to air. This is the amount of energy the object has to dispense when it hits the ground. (g is the acceleration due to gravity at sea level = 9.8m/s^2)

The force with which it hits the ground depends on elastic properties of the object, ie., how much of the energy is wasted in deformation, frictional heat, etc. Whatever energy is not wasted in these endeavours is associated with the inelastic force between the ground and the object.

A more useful thing to observe is the change in momentum of the object. Assuming the object is very inelastic and dispenses a minimum of its energy due to deformation or heat, we have the kinetic energy (1/2)mv^2 = Wd = mgd, so v = Sqrt(2gd) is the velocity with which it impacts the ground, while m*Sqrt(2gd) is the momentum it carries before it hits the ground. Force is change in momentum over time, so we have F = (W/(Tg))Sqrt(2gd) where T is the time it takes the object to decelerate to 0. This is why cushioning and crumple zones are important in decreasing the force imparted to people in car accidents, etc.

Wiki User

15y ago

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Q: How do you find the force with which something hits the ground if you know the distance and weight?
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