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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.

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

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You can't. Work is (force) times (distance), so you have to know something about the force. Just knowing the mass doesn't tell you anything about the force ... unless there's actually something else about the mass that you've overlooked.

Weight has same dimension and unit as force. Distance has same dimension and unit as displacement. So weight * distance has same dimension and unit as force * displacement. Force * displacement is work done by the force. Work divided by time to do the work is Power. So weight * distance divided by time also has same dimension and unit as Power although it is not power. S.I. unit of weight * distance divided by time is Newton *meter/second or Nms-1 (in abbr.) It's dimensions are 1, 2, -3 in mass, length and time respectively. Note that given quantity's unit can't be joule/second or watt because weight * distance is not work done, only unit and dimension are same1 . 1. Two physical quantities may have same dimensions and units but that doesn't mean they refer to same quantity.

I usually start with the definition of work: Work = force * distance so... Force = work / distance Distance = work / force So, no. You had it backwards.

In physics, work = force x distance.

With extreme difficultly as they measure different things: mass is a measure of how much something weighs*, whereas length is a measure of distance. * Actually weight is the force on a mass due to acceleration and is measured in Newtons. However, weight and mass are often, incorrectly, used interchangeably and I cannot think of a better word to describe mass. To further muddy the waters, mass and distance ARE related by energy and acceleration: energy = (mass × acceleration) × distance which can be rearranged to distance = energy ÷ (mass × acceleration) So for an object given a mass, an acceleration (on earth acceleration due to gravity is a good one) and an amount of energy put in, the distance the object is moved (by that energy [in acting as a force]) can be calculated.

Related questions

Work = force * distance moved

The weight of the crate is acting downward on the ground and the ground is exerting a force equal to the weight of the crate upward on the crate.

A force is pushing or pulling on something.

The weight of the crate is acting downward on the ground and the ground is exerting a force equal to the weight of the crate upward on the crate.

A

Work is something that is done when a force moves an object over a distance.

Work is something that is done when a force moves an object over a distance.

The object's mass and weight determines the force and distance, the greater the force, the less distance it covers. However, when a knife cuts the object, it covers less force and more distance.

The force (weight) between the person and earth diminishes with distance. eg double the distance, quarter the force.

When you stand still . . . The sole of your shoe exerts a downward force equal to your weight against the ground. The ground exerts an upward force equal to your weight against the sole of your shoe. The net force where the sole of your shoe meets the ground is zero, which is the reason that your shoe doesn't accelerate vertically.

Torque is the combination of perpendicular distance and weight; it is not a true force

When you stand still . . . The sole of your shoe exerts a downward force equal to your weight against the ground. The ground exerts an upward force equal to your weight against the sole of your shoe. The net force where the sole of your shoe meets the ground is zero, which is the reason that your shoe doesn't accelerate vertically.