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? Thanks for your help.
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 That page is the table of contents for pages including these: 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/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.