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### Force of a Falling Object

```Date: 12/27/2002 at 20:12:35
From: Rusty
Subject: Force

I am in 10th grade and I would like to figure out the force of a
falling object. I have been trying to figure this out for something
like 5 or 6 months.

Here's the question: If a 10-lb. bowling ball is dropped from 100
feet, how hard will it hit the ground?

```

```
Date: 12/27/2002 at 20:47:26
From: Doctor Jeremiah
Subject: Re: Force

Hi Rusty,

The acceleration while it's falling is 32 ft/sec^2, but the
acceleration you are interested in is the deceleration when it hits.
How long does it take to go from whatever speed it is moving when it
just touches until it stops moving?

There are two factors:  How much does the ground give way, and how
much does the object give way? Say the object takes a 10th of a second
to stop moving after it hits (a guess because it really depends on the
elasticity of the object and the ground).

The next bit is important: pounds (lb) measure weight, not mass.  1
slug of mass weighs 1 pound on Earth because 1 pound (lb) = 1 slug x
32 feet/sec^2. So I am going to use slugs for mass and pounds for
weight. (You can use pounds where mass is asked for as long as you are
on the Earth, where the acceleration due to gravity is 32 feet/sec^2.)

In metric, kilograms (kg) are used for mass and Newtons (N) are used
for weight.

If a ball with 10 slugs of mass (10 pounds of weight) is moving 96
feet/sec when it hits, then its momentum just as it touches is mass
times velocity or 960 slug feet/sec. The impulse imparted to the
ground is the change in momentum (from 960 slug feet/sec to 0 slug
feet/sec). But the impulse is also the force applied multiplied by the
time it's applied. The decelerating force is applied for 0.1 seconds
because that's how long it takes to stop.

force x time = mass x (ending velocity - starting velocity)
force x 0.1 sec = 10 slugs x (0 ft/sec - 96 ft/sec)
force x 0.1 sec = -960 slug ft/sec
force = -960 slug ft/sec / 0.1 sec
force = -9600 slug ft/sec^2

Take a look at these pages for more detail (the units are in metric,
but that doesn't change how it works):

Momentum and Its Conservation - The Physics Classroom
http://www.physicsclassroom.com/Class/momentum/momtoc.html

momentum
http://www.physicsclassroom.com/Class/momentum/U4L1a.html

impulse
http://www.physicsclassroom.com/Class/momentum/U4L1b.html

Let me know if you want to talk about momentum and impulse some more.

- Doctor Jeremiah, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Physics/Chemistry

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