Linear Momentum
Momentum – a quantity defined as the product of the mass and velocity of an object
Example 1
Rich Gossage set a fastball record by hurling a 0.14 kg baseball at a speed of 46.3 m/s. What was the magnitude of the ball’s momentum as it left his hand?
Impulse
Impulse – the product of the force and the time over which the force acts on an object
Impulse – Momentum Theorem
Example 2
A 0.149 kg baseball traveling at 28 m/s due south approaches a waiting batter. The ball is hit and momentarily crushed to almost half its original size in a collision with the bat lasting a few milliseconds. The ball springs back, sailing away at 46 m/s due north. Determine the magnitudes of its initial and final momenta and the change in its momentum.
Example 3
If the maximum coefficient of kinetic friction between a 2300 kg car and a road is 0.50, what is the minimum stopping distance for a car moving at 29 m/s?
Example 4
A 0.55 kg ball approaches a wall perpendicularly with a speed of 17 m/s and rebounds in the opposite direction with a speed of 15 m/s. What is the impulse exerted on the wall?
Conservation of Momentum
| Momentum in a Collision | ||||||
|---|---|---|---|---|---|---|
| Ball A | Ball B | |||||
| Mass | Velocity | Momentum | Mass | Velocity | Momentum | |
before collision |
0.16 kg |
4.50 m/s |
0.72 kg•m/s |
0.16 kg |
0 m/s |
0 kg•m/s |
after collision |
0.16 kg |
0.11 m/s |
0.018 kg•m/s |
0.16 kg |
4.39 m/s |
0.70 kg•m/s |
Conservation of Momentum: The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.
Conservation of Momentum Video
Example 5
According to published figures, a bullet fired from a 9 mm Luger having a mass of 8.0 g, and a muzzle speed of 1155 ft/s. If the mass of the gun is 0.90 kg, what is its recoil speed when the gun is fired horizontally? Ignore the escaping gases.
Collisions
Perfectly Inelastic Collisions – a collision in which two objects stick together after colliding
Example 6
During a rainy day football game, a 192 lb quarterback is standing holding the ball looking for a receiver when he’s unkindly hit by a 288 lb tackle charging in at 6.1 m/s. (a) At what speed do the two men, tangled together, initially sail off onto the wet field? Assume friction is negligible and that the impact is head-on. (b) How much mechanical energy is lost to friction?
Elastic Collisions – a collision in which the total momentum and the total kinetic energy are conserved
Example 7
Cart A, with mass of 0.355 kg, moves along a frictionless air track with a velocity of 0.095 m/s left. It collides with Cart B, with mass of 0.710 kg and a speed of 0.045 m/s in the same direction. After collision, Cart A continues in the same direction at 0.035 m/s. What is the speed of Cart B?
Example 8
A 2.00 kg ball, A, is moving at a speed of 5.00 m/s. It collides with a stationary ball, B, of the same mass. After collision, A moves off in a direction 30.0˚ to the left of its original direction. Ball B moves off in a direction 90.0˚ to the right of ball A’s final direction. How fast are they moving after collision?