Momentum Worksheet answers

1. m1v1 + m2v2 = (m1 + m2)v2 (10 tons)(4 m/s) + (30 tons)(0 m/s) = (10 tons + 30 tons)v2 40 + 0 = 40v2 40 = 40v2 V2 = 1 m/s (Note: do not have to convert tons to kilograms. The units cancels out at the end)

2. A 2 kg blob of putty moving at 4 m/s slams into a 6 kg blob of putty at rest. What is the speed of the two stuck-together blobs immediately after colliding? m1v1 + m2v2 = (m1 + m2)v2 (2 kg)(4 m/s) + (6 kg)(0 m/s) = (2 kg + 6 kg)v2 8 + 0 = 8 v2 8 = 8 v2 V2 = 1 m/s

3. A football player runs at 8 m/s and plows into a 80 kg referee standing on the field causing the referee to fly forward at 5.0 m/s. If this were a perfectly elastic collision, what would the mass of football player be? m1v1 + m2v2 = m1v1 + m2v2 (m kg)(8 m/s) + (80 kg)(0 m/s) = (m kg)(0) + 80 kg(5) 8m= 400 m = 50 kg

4. Assuming that this is a perfect inelastic collision, calculate the velocity after the collision in the example below. m1v1 + m2v2 = (m1 + m2)v2 (80 kg)(6 m/s) + (40 kg)(0 m/s) = (80 kg + 40 kg)v2 480 + 0 = 120v2 480 = 120v2 V2 = 4 m/s

5. A large locomotive with a mass 4 kg collides into a 1 kg motionless railroad car collides and couples together. What is their combined speed after the collision? m1v1 + m2v2 = (m1 + m2)v2 (4 m)(5 km/hr) + (m)(0 km/hr) = (4m + m)v2 20m km/hr + 0 m km/hr = 5mv2 20m km/hr = 5m v2 V2 = 4 km/hr

6. A 2.0 kg mass is moving on a frictionless airtrack. It collides into a motionless 1.5 kg mass. What is the the combined speed of the two masses if they stick together on impact? m1v1 + m2v2 = (m1 + m2)v2 (2 kg)(1.5 m/s) + (1.5 kg)(0 m/s) = (2 kg + 1.5 kg)v2 3.0 kg m/s + 0 = 3.5 kg v2 3 kg m/s = 3.5 m/s v2 V2 = 0.86 m/s

7. A 1000 kg car is rolling down the street at 2.5 m/s. How fast would a 2500 kg car have to be to collide into it in order to bring it to rest (0 m/s)? m1v1 + m2v2 = (m1 + m2)v2 (1000 kg)(2.5 m/s) + (2500 kg)(v2) = (1000 kg + 2500 kg) (0 m/s) 2500 kg m/s + 2500 v2 = 0 2500 v2 = -2500 kg m/s V2 = -1 m/s

8. A railroad car slams into another railroad car and couples together. What is the combined speed of the railroad cars after the collision? m1v1 + m2v2 = (m1 + m2)v2 (4000 kg)(2 m/s) + (6000 kg)(0 m/s) = (4000 kg + 6000 kg)v2 8000 + 0 = 10000v2 8000 = 10000v2 V2 = 0.8 m/s

9. Two blocks moving in opposite directions collide and stick together after the collision. What is their combined speed after the collision? m1v1 + m2v2 = (m1 + m2)v2 (1 kg)(8 m/s) + (2 kg)(-1 m/s) = (1 kg + 2 kg)v2 8 + (-2) = 3 v2 6 = 3 v2 V2 = 2 m/s

10. An explosion causes the cars to move apart from each other. According to the diagram below, what is the velocity of each of the cars as they move away from each other? (m1 + m2)v = m1v1 + m2v2 0 = m1v1 + m2v2 m1v1 = -m2v2 (since the masses are equal) v1 = -v2

11. A 3000-kg truck moving rightward with a speed of 5 km/hr collides head-on with a 1000-kg car moving leftward with a speed of 10 km/hr. The two vehicles stick together and move with the same velocity after the collision. Determine the post-collision speed of the car and truck. m1v1 + m2v2 = (m1 + m2)v2 (3000 kg)(5 km/hr) + (1000 kg)(-10 km/hr) = (3000 kg + 1000 kg)v2 15000+ (-10000) = 4000 v2 5000 = 4000 v2 V2 = 1.25 km/hr

12. During a goal-line stand, a 75-kg fullback moving eastward with a speed of 10 m/s collides head-on with a 100-kg lineman moving westward with a speed of 4 m/s. The two players collide and stick together, moving at the same velocity after the collision. Determine the post collision velocity of the two players. m1v1 + m2v2 = (m1 + m2)v2 (75 kg)(10 m/s) + (100kg)(-4 m/s) = (75 kg + 100 kg)v2 750 + (-400) = 175 v2 350 = 175 v2 V2 = 2 m/s

13. Calculate the velocity of the rifles recoil after firing. (m1 + m2)v = m1v1 + m2v2 (4 kg + 0.01 kg)(0 m/s) = 4kg v1 + (0.01 kg)(300 m/s) 0 = 4kg v1 + 3 kg m/s 4kg v1 = -3 kg m/s v1 = -0.75 m/s

14. What is the velocity of the "8" ball after the elastic collision below? m1v1 + m2v2 = m1v1 + m2v2 (0.25 kg)(2 m/s) + (0.25 kg)(0 m/s) = (0.25 kg)(0 m/s) + (0.25 kg)v2 0.5 + 0 = 0.25v2 0.5 = 0.25v2 V2 = 2 m/s

15. A 6000 kg railroad car moving at 5 m/s collides into a stationary car with a mass of 4000 kg. If they couple together after the collision, what will be their combined velocity immediately after impact? m1v1 + m2v2 = (m1 + m2)v2 (6000 kg)(5 m/s) + (4000 kg)(0 m/s) = (6000 kg + 4000 kg)v2 30000 + 0 = 10000v2 30000 = 10000v2 V2 = 3 m/s