Online Test Banks
Score higher
See Online Test Banks
eLearning
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

How to Find the Velocity of an Object before Collision

In physics, the principle of conservation of momentum comes in handy when you can’t measure velocity with a simple stopwatch. Say, for example, that you accept a consulting job from an ammunition manufacturer that wants to measure the muzzle velocity of its new bullets. No employee has been able to measure the velocity yet, because no stopwatch is fast enough. What do you do? You decide to arrange the setup shown in the figure, where you fire a bullet of mass m1 into a hanging wooden block of mass m2.

Shooting a wooden block on a string allows you to experiment with velocity, but don’t try thi
Shooting a wooden block on a string allows you to experiment with velocity, but don’t try this at home!

The directors of the ammunition company are perplexed — how can your setup help? Each time you fire a bullet into a hanging wooden block, the bullet kicks the block into the air. So what? You decide they need a lesson on the principle of conservation of momentum. The original momentum, 
you explain, is the momentum of the bullet:

pi = mvi

Because the bullet sticks in the wooden block, the final momentum is the product of the total mass, m1 + m2, and the final velocity of the bullet/wooden block combination:

pf = (m1 + m2)vf

Because of the principle of conservation of momentum, you can say that

pf = pi

Therefore, you can plug in the earlier expressions for final and initial momentum:

image1.png

The directors start to get dizzy, so you explain how the initial kinetic energy of the block after it’s struck (with the bullet lodged inside it) goes into its final potential energy when it rises to height h. Here’s how you can represent the block-plus-bullet’s initial kinetic energy and the bullet-and-block’s change in potential energy:

image2.png

You can plug in the value of vf, which gives you

image3.png

With a flourish, you explain that solving for vi gives you the bullet’s initial velocity:

image4.png

This should be simplified to:

image5.png

You measure that the bullet has a mass of 50 grams, that the wooden block has a mass of 10.0 kilograms, and that upon impact, the block rises 50.0 centimeters into the air. Plugging in those values gives you your result:

image6.png

The initial velocity is 630 meters per second, which converts to about 2,070 feet per second. “Brilliant!” the directors cry as they hand you a big check.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Advertisement

Inside Dummies.com

Dummies.com Sweepstakes

Win $500. Easy.