Recoil
Conservation of Momentum
Recoil Problem — when interacting objects start from rest
Review – Explain this using one of Newton's Laws
A lead brick has a lot of mass and therefore a lot of inertia.
The greater the mass, the greater the tendency for an object to remain at rest, the smaller the acceleration that is produced by a given force.
Conservation of Momentum
Newton Collider
B) Recoil Problem
When interacting objects start from rest
"What is the total momentum before cannon is fired?"
"Total momentum after clown is fired?"
"Total momentum before = 0. (at rest)"
"Total momentum after = 0. (momenta are equal but opposite.)"
"In real life, it would be foolish to shoot a rifle like this. Why?"
"The recoil on that rifle would throw the shooter's shoulder out!"
Ex 1) Rifle Recoil
After rifle is fired
| Rifle | Bullet |
|---|---|
| mR = 4.0 kg | mB = 5.0 × 10-3 kg |
| VR = ? | VB = 500. m/s |
Total Momentum Before = Total Momenta After Interaction
0 = m1V1 + m2V2
Subtract m2V2 from both sides:
m1v1 = −m2V2
In problem solving, remove the negative sign and use:
(4.0 kg)V = (5.0 × 10-3 kg)(500. m/s)
(4.0 kg)V = 2.5 kg·m/s
Equal vs. Unequal Mass Explosions
Yes, the slower cart has a greater mass.
Ex 2) Magnet Momentum
When the string holding them together is cut, they move apart under a magnetic force of repulsion.
a) What is the total momentum of the magnets before the string is cut?
Total momentum before = 0
(Both objects begin at rest)
b) What is the total momentum of the magnets after the string is cut?
Total momentum after = 0
(Total mom. before = Total mom. after)
c) What is the velocity of the 1.0 kg mass when the velocity of the 2.0 kg magnet is 30. m/s?
| Magnet 1 | Magnet 2 |
|---|---|
| m1 = 2.0 kg | m2 = 1.0 kg |
| V1 = 30. m/s | V2 = ? |
2.0 kg(30. m/s) = 1.0 kg(V)
One More
What is the velocity of the cannon below?
500 kg(V1) = 100 kg(15 m/s)
Related
Enrichment
Rifle Recoil
Dr. Dave's Hall of Fame
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. A cannon at rest fires a ball. What is the total momentum of the cannon and ball just after firing?
2. A 4.0 kg rifle fires a 5.0 × 10⁻³ kg bullet at 500. m/s. What is the rifle's recoil speed?
3. Two magnets at rest push apart. The 2.0 kg magnet moves at 30. m/s. How fast does the 1.0 kg magnet move?
4. A 500 kg cannon fires a 100 kg ball at 15 m/s. What is the cannon's recoil speed?
5. Two carts at rest are pushed apart by a spring. One cart moves away more slowly. What does that tell you?
Rifle Recoil
At a target range, a 4.0-kg rifle fires a 0.010-kg bullet. The bullet leaves the barrel at 800. m/s. Before firing, the rifle and bullet are at rest.
What is the recoil speed of the rifle if it is free to move?
▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)
Challenge score: 0 / 6
C1. The bullet is fired to the right. The bullet takes 0.0020 s to accelerate along the barrel. Choose the direction of the average force the bullet exerts on the rifle, and determine its magnitude.
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C2. Why do shooters press the rifle firmly against their shoulder?
C3. A 76-kg shooter holds the 4.0-kg rifle firmly against his shoulder so that rifle and shooter recoil together. Substitute numerical values into a mathematical representation that can be used to determine the recoil speed of the rifle–shooter combination. Then calculate the speed.
C4. A student makes the following claim.
Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.
C5. What are the kinetic energies of the bullet and the free rifle just after firing?
C6. A rifle designer considers making the rifle heavier to reduce recoil. Identify one benefit and one drawback of this design change, using momentum to explain the benefit.