##### ie-Physics
Impulse And Momentum

### Summary and Practical Applications of Physics Skills

##### © by William Dietsch 2004 ### Momentum

•   Momentum is a dynamical quantity, carried by all material objects, while in motion.   In physics, momentum is the calculated product of the scalar mass of a body and its vector velocity.   All moving bodies have momentum, regardless of their size or velocity.   The rules of momentum apply universally to all objects in the universe.  As with many scientific terms, momentum is often adopted by the general public with wider meanings describing things such as political fortune (e.g., Candidate X's campaign is gaining momentum) or the progress of sporting event (e.g., Team Y seems to have momentum on its side.).   The definition of momentum in physics is much more specific and precisely defined by mathematics.

•   An object with a large mass and low velocity can have a momentum equal to an object with a small mass and a high velocity.

•   The simple laws of momentum do not distinguish between the aforementioned objects, if the products of mass and velocity are equal, they are treated as identical.

•   Equation for the calculation of the momentum P (units of kg m/s) of a body with velocity v (units of m/s) and mass m (units of kg) is:

P = mv.

### Impulse

•   Impulse describes the cause of momentum changes.   The calculated product of a force and the duration of its application (time in seconds) is equal to the impulse.  The equation for the calculation of impulse by the application of a force F (units of Newtons) for a duration of time Δt (units of seconds) is:

I = F Δt = Δ P

•   Impulse causes a corresponding change in the momentum of a body.

### Conservation Of Momentum In Explosions And Collisions

When bodies interact, in a closed system (no external forces act on a closed system from outside), the vector sum of the momenta BEFORE the interaction is equal to the vector sum of the momenta AFTER the interaction.

•   Collisions occur when two or more objects strike each other at some central point of impact.

It may be a sign that a collision is elastic when the bodies move freely apart after colliding.  An example of a (nearly) elastic collision is when billiard balls hit together and move off separately.  When the objects in the collision remain entangled after colliding, it is a sign that the collision is inelastic.   An examples of an inelastic collision is when a train car collides with another and they couple or when a paintball sticks to its target.  (Usually elastic is defined in terms of conservation of mechanical energy, a topic discussed later.)

When objects fly apart from rest or a center of mass, an explosion is said to have occurred.   The obvious example of an explosion is a bomb sending pieces flying apart.   The individual fragments carry momentum but the vector sum of all momenta in the explosion is equal to the starting momentum (zero with respect to the center of mass).   Jump from a canoe and it moves away from you, is a less expected example of an explosion.

### Impulse And Momentum Problems:

1. A 23.5 N force acts on a body for duration of 12.0 s.   Compute the impulse that the body receives.   How long does a force of 14.0 N need to act in order to impress the same impulse on the body?

2. A 2.5 kg body has a velocity of 5.8 m/s.   How long will it require to stop if a breaking force of 2.3 N acts on it?

3. A motorcycle has a mass of 325 kg and has an initial velocity of 5.6 m/s.   A force of 62 N acts on the machine and causes its velocity to increase to 28 m/s.   How long does the force act on the machine?

4. A small car has a mass of 853 kg and a speed of 120 km/h.   Compute the momentum of the car.

5. A 0.25 kg ball approaches a player at +6.2 m/s.   The player kicks the ball and gives it a velocity of -12 m/s.   If the player's foot is in contact with the ball for 0.021 s, compute the average force exerted on the ball.

6. A force of 1500 N is required to stop a car moving at an initial speed of 26 m/s in 21 s.   Compute the mass of the car.

7. A 15,000 kg train car is rolling at a speed of 3.2 m/s.   Compute the time required for a force of 1200 N to stop the car.

8. A car moving at 11 m/s crashes into an obstacle and stops in 0.26 s.   Compute the force that a seatbelt exerts on a 21 kg child to bring him/her to a stop.

### Conservation Of Momentum Problems:

Identify the type of problem using EC for elastic collision, IC for inelastic collision, and EX for explosions.   All of the following problems are one-dimensional.   That allows us to use + for motion to the right and - for motion to the left.  (Many momentum problems allow for this simple treatment of their vector momenta by carefully choosing a suitable frame of reference.)

1. A 0.018 kg ball moving at +48 m/s is caught by a 81 kg person standing on a frictionless surface.   Compute the speed of the person after the ball is caught.

2. A 0.038 kg bullet strikes a stationary 5.0 kg block of wood and embeds itself (sticks in it).   The block flies off at a speed of 8.8 m/s.   Compute the speed of the bullet.

3. A 0.50 kg ball with a velocity of +6.0 m/s collides head on with a 1.0 kg ball moving in the opposite direction at -12.0 m/s.   The 0.50 kg ball moves off at -14 m/s after impact.   Compute the velocity of the 1.0 kg ball.

4. A 98 kg running back, running at 8.7 m/s, collides in mid air with a 130 kg tackle moving in the opposite direction.   If the final velocity of the two players is zero, compute the initial velocity of the tackle.

5. Ball A with a mass of 5.0 kg, moves at a velocity of 0.20 m/s.   It collides with ball B, mass 10.0 kg moving in the same direction at 0.10 m/s.   If the velocity of ball A is 0.08 m/s after the collision, compute the final velocity of ball B.

6. A 2800 kg SUV moving at some speed hits the rear end of a 950 kg car at rest.   After the collision, they remain entangled and move off at 9.1 m/s.   Compute the initial speed of the SUV.

7. A 15 g bullet is fired into a 5.10 kg block at rest.   After impact, the bullet and block move off at 1.0 m/s.   Compute the initial speed of the bullet.

8. A car with a mass of 1350 kg, moving at a speed of 31 m/s, strikes a stationary 2170 kg car.   If the cars remain together after the crash, compute the speed of the wreck.

9. A 6.0 g bullet moving at +120 m/s hits a stationary 5.20 kg block and ricochets in the opposite direction with speed of -110 m/s.   Compute the speed of the block after the impact.

10. A 5.2 kg rocket shoots 0.89 kg of exhaust gas out of its engine with an average velocity of 755 m/s.   Compute the speed of the rocket.

11. A 1.5 kg cart flies apart at 0.27 m/s from an explosion with a 4.5 kg cart.   What is the velocity of the 4.5 kg cart?

12. An 80 kg camper jumps from a 45 kg canoe.   If the velocity of the camper is 4.0 m/s, what is the velocity of the canoe in the opposite direction?   Has this ever happened to you?

13. A 225 kg cannon fires a 5.1 kg projectile with a muzzle velocity of 850 m/s.   Compute the recoil velocity of the cannon. next experiment: Experiment III-3