Momentum And Impulse

1. An object is pushed with a force of 6.0 N for 0.50 s. What impulse is given to it? 3.0 kg•m/s

2. What impulse produces a velocity change of 4.00 m/s in a 12.5 kg mass? Δp=p_final – p_initial = mΔv = 50.0 N•s

3. A 15.0 kg wagon is accelerated by a constant force of 60.0 N from 5.00 m/s to 13.00 m/s.

(a) What impulse does the wagon receive? 120 N•s

(b) For how long was the force acting on the wagon? 2.0 s

4. A freight car with a mass of 6.0 x 10⁴ kg is rolling along a level track at 0.40 m/s, dragging a chain behind it.

(a) If the largest force that could be applied to the chain is 320.0 N, how long would it take to stop the car? Δt = Δp/F = 75 seconds

(b) How far would the car move before it could be stopped? Use kinematics equation, acceleration is -5.33 x 10^-3 m/s², therefore, 15.0 m

5. What average force will stop a hammer with a momentum of 48.0 N•s in 0.030 s? 1600 N

6. A stone of mass 10.0 kg slides along the ice in a straight line with a constant velocity of 8.00 m/s. A constant force then acts on the stone for 2.50 s, changing its velocity to 2.00 m/s.

(a) What is the momentum of the stone before and after the force acts? Before is 80.0 kg•m/s while after is 20.0 kg•m/s

(b) Calculate the impulse acting on the stone. Δp = 60.0 kg•m/s

(c) What is the magnitude and direction of the force that is acting? The force is 24.0 N opposing the original motion (and momentum).

7. Two frictionless discs on an air table, initially at rest, are drive apart by an explosion with velocities of 9.0 m/s and 5.0 m/s. What is the ratio of their masses? p_initial is zero, after explosion masses go in opposite directions and have MUST have equal but oppositely directed momenta. The masses have to be in a 5:9 ratio in order to make the momenta equal. Best way to see this is as m₂=⁵/₉m₁.

8. Two dynamic carts are at rest with a compressed spring between them. When the spring is allowed to expand, the carts move apart. Both hit bricks at either end of the table, simultaneously, but cart A moves 0.60 m while cart B moves 0.90 m. What is the ratio of:

(a) the speed of A to the speed of B after the expansion of the spring? Cart B must be moving faster since it went a further distance in the same amount of time as cart A. The ratio is 3:2. Best way to see this is as m₂=³/₂m₁.

(b) their masses? Since each cart acquired the same momentum (equal but opposite since there was initially zero momentum), the ratio of the masses of the carts is 3:2 (Cart A: Cart B). Cart A is more massive than B, noted by the fact that cart A moves a smaller distance and has lees speed (but same momentum).

(c) the impulses applied to the carts? The impulses (read this as the change in momentum or Δp) would have to be equal.

(d) the acceleration of the carts while the spring was pushing them apart? Since acceleration is the change in velocity over time, Cart B must have greater acceleration … again in a 3:2 ratio.

9. A proton of mass 1.67 x 10^-27 kg, traveling with a speed of 1.0 x 10⁷ m/s, collides with a helium nucleus at rest. The proton rebounds straight back with a speed of 6.0 x 10⁶ m/s while the helium nucleus moves forward with a speed of 4.0 x 10⁶ m/s.

(a) What was the total momentum before the collision? 1.67 x 10^-20 kg•m/s

(b) What was the momentum of the proton after the collision? 1.00 x 10^-20 kg•m/s in opposite direction!

(d) Determine the mass of the helium nucleus. 6.68 x 10^-27 kg

10. A stationary flatcar of mass 4.0 x 10⁴ kg is rammed by a locomotive with a mass of 6.0 x 10⁴ kg and a velocity of 4.5 m/s. If they stick together, with what velocity will they continue to move? 2.7 m/s

11. Two 2.5 kg carts are moving along together with a velocity of 2.0 m/s when a spring compressed between them expands rapidly. The front cart continues with a velocity of 3.0 m/s, in the same direction.

(a) What was the momentum of the two carts before the explosion? 10. kg•m/s

(b) What was the momentum of the front cart after the explosion? 7.5 kg•m/s

(d) What velocity would the front cart have had to acquire for the second cart to remain stationary after the explosion? 4.0 m/s

12. A 1.5 kg brick is dropped vertically onto a 2.5 kg toy truck, which is moving across a level floor at 0.80 m/s. With what velocity do the truck and brick continue to move, after the brick has landed on the truck? 0.50 m/s

13. Explain how an astronaut who is stranded in free space a short distance from his spacecraft might employ his knowledge of momentum to return safely to the craft. Why must he be very careful about his momentum? He or she may have to throw something away from themself (directly away from the direction that they would like to head) in order to gain momentum towards the spacecraft. The astronaut must be careful since, without the effects of gravity and/or something to grab onto, he/she could find themselves carrying on in a straight line forever – the astronaut must make sure that their momentum is lines up correctly in order not to miss the shuttlecraft!

14. A sandbag is mounted on a cart that is at rest on a horizontal frictionless surface, and their total mass is 4.5 kg. What will be the velocity of the cart and sandbag if a bullet of mass 2.0 g is fired into the sandbag with a horizontal velocity of 500. m/s? The p of the bullet is 1.0 N•s. This will be transferred to the sandbag etc (note that the bullet’s mass is too small to worry about in comparison to the other masses). The momentum of the sandbag etc will now be 1.0 N•s, which gives it a velocity of 0.22 m/s.

15. Two boys of mass 45 kg and 60 kg, respectively, are sitting on two separate 15 kg wagons, facing each other and holding a rope taut between them. The lighter boy pulls on the rope and acquires a velocity of 2.0 m/s. What is the velocity of the other boy? 1.6 m/s towards the lighter boy.