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We will work backwards to find an expression for v. 0 . Page 2. Mechanical energy conservation? ... set the bullet's kinetic energy before the collision to.
Typology: Schemes and Mind Maps
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A ballistic pendulum is a device used to measure the speed of a bullet. A bullet of mass m is fired at a block of wood (mass M ) hanging from a string. The bullet embeds itself in the block, and causes the combined block plus bullet system to swing up a height h. What is v 0 , the speed of the bullet before it hits the block? We will work backwards to find an expression for v 0
Mechanical energy is conserved in the pendulum motion after the collision. Work backwards, starting with the swing of the pendulum just after the collision until it reaches its maximum height, h. Write out the five-term energy-conservation equation. Eliminate terms that are zero. Substitute expressions for these terms:
Solve for the speed of the pendulum at its lowest point. We get the familiar expression: This is the final velocity of the system after the collision. In our collision analysis, then, we have:
If we use the following: Mass of the bullet: m = 30 grams Mass of the block: M = 870 grams Maximum height: h = 0.74 m We find that:
Look at the ratio of the kinetic energy after the collision to the kinetic energy before the collision: From momentum conservation: In our numerical example, this ratio is 0.033. 3.3% of the mechanical energy remains. 96.7% is lost!
How fast is ball A going, just before the collision? Apply energy conservation. Eliminate three of the terms.
We can use the same equation afterwards. For ball A afterwards: For ball B afterwards:
Apply momentum conservation. How do we account for the fact that momentum is a vector?
Apply momentum conservation. How do we account for the fact that momentum is a vector? Choose a positive direction (to the right), so the velocity of ball A after the collision is negative.
Kinetic energy before the collision: 32 J Kinetic energy after the collision: 8 J + 12 J = 20 J The kinetic energy is smaller after the collision, so the collision is inelastic. It is not completely inelastic, because the two balls do not stick together after the collision.
