

Lesson 1: The Impulse Momentum Change TheoremMomentum and Impulse Connection Lesson 2: The Law of Momentum ConservationMomentum Conservation Principle Momentum Conservation in Collisions Eq'ns as a "Recipe" for Problem Solving
Momentum Conservation in
Explosions 
Lesson 1: The ImpulseMomentum Change TheoremMomentum and Impulse ConnectionAs mentioned in the previous part of this lesson, momentum is a commonly used term in sports. When a sports announcer says that a team has the momentum they mean that the team is really on the move and is going to be hard to stop. The term momentum is a physics concept. Any object with momentum is going to be hard to stop. To stop such an object, it is necessary to apply a force against its motion for a given period of time. The more momentum which an object has, the harder that it is to stop. Thus, it would require a greater amount of force or a longer amount of time or both to bring such an object to a halt. As the force acts upon the object for a given amount of time, the object's velocity is changed; and hence, the object's momentum is changed. The concepts in the above paragraph should not seem like abstract information to you. You have observed this a number of times if you have watched the sport of football. In football, the defensive players apply a force for a given amount of time to stop the momentum of the offensive player who has the ball. You have also experienced this a multitude of times while driving. As you bring your car to a halt when approaching a stop sign or stoplight, the brakes serve to apply a force to the car for a given amount of time to change the car's momentum. An object with momentum can be stopped if a force is applied against it for a given amount of time. A force acting for a given amount of time will change an object's momentum. Put another way, an unbalanced force always accelerates an object  either speeding it up or slowing it down. If the force acts opposite the object's motion, it slows the object down. If a force acts in the same direction as the object's motion, then the force speeds the object up. Either way, a force will change the velocity of an object. And if the velocity of the object is changed, then the momentum of the object is changed. These concepts are merely an outgrowth of Newton's second law as discussed in an earlier unit. Newton's second law (F_{net }= m • a) stated that the acceleration of an object is directly proportional to the net force acting upon the object and inversely proportional to the mass of the object. When combined with the definition of acceleration (a = change in velocity / time), the following equalities result. If both sides of the above equation are multiplied by the quantity t, a new equation results. This equation represents one of two primary principles to be used in the analysis of collisions during this unit. To truly understand the equation, it is important to understand its meaning in words. In words, it could be said that the force times the time equals the mass times the change in velocity. In physics, the quantity Force • time is known as impulse. And since the quantity m•v is the momentum, the quantity m•v must be the change in momentum. The equation really says that the













Observe that each of the collisions above involve the rebound of a ball off a wall. Observe that the greater the rebound effect, the greater the acceleration, momentum change, and impulse. A rebound is a special type of collision involving a direction change in addition to a speed change. The result of the direction change is a large velocity change. On occasions in a rebound collision, an object will maintain the same or nearly the same speed as it had before the collision. Collisions in which objects rebound with the same speed (and thus, the same momentum and kinetic energy) as they had prior to the collision are known as elastic collisions. In general, elastic collisions are characterized by a large velocity change, a large momentum change, a large impulse, and a large force.
Use the impulsemomentum change principle to fill in the blanks in the following rows of the table. As you do, keep these three major truths in mind:
Click the button to view answers.










































There are a few observations which can be made in the above table which relate to the computational nature of the impulsemomentum change theorem. First, observe that the answers in the table above reveal that the third and fourth columns are always equal; that is, the impulse is always equal to the momentum change. Observe also that the if any two of the first three columns are known, then the remaining column can be computed. This is true because the impulse=force • time. Knowing two of these three quantities allows us to compute the third quantity. And finally, observe that knowing any two of the last three columns allows us to compute the remaining column. This is true since momentum change = mass • velocity change.
There are also a few observations which can be made which relate to the qualitative nature of the impulsemomentum theorem. An examination of rows 1 and 2 show that force and time are inversely proportional; for the same mass and velocity change, a tenfold increase in the time of impact corresponds to a tenfold decrease in the force of impact. An examination of rows 1 and 3 show that mass and force are directly proportional; for the same time and velocity change, a fivefold increase in the mass corresponds to a fivefold increase in the force required to stop that mass. Finally, an examination of rows 3 and 4 illustrate that mass and velocity change are inversely proportional; for the same force and time, a twofold decrease in the mass corresponds to a twofold increase in the velocity change.
Express your understanding of the impulsemomentum change theorem by answering the following questions. Click the button to view the answers.
1. A 0.50kg cart (#1) is pulled with a 1.0N force for 1 second; another 0.50 kg cart (#2) is pulled with a 2.0 Nforce for 0.50 seconds. Which cart (#1 or #2) has the greatest acceleration? Explain.
Which cart (#1 or #2) has the greatest impulse? Explain.
Which cart (#1 or #2) has the greatest change in momentum? Explain.
2. In a physics demonstration, two identical balloons (A and B) are propelled across the room on horizontal guide wires. The motion diagrams (depicting the relative position of the balloons at time intervals of 0.05 seconds) for these two balloons are shown below.
Which balloon (A or B) has the greatest acceleration? Explain.
Which balloon (A or B) has the greatest final velocity? Explain.
Which balloon (A or B) has the greatest momentum change? Explain.
Which balloon (A or B) experiences the greatest impulse? Explain.
3. Two cars of equal mass are traveling down Lake Avenue with equal velocities. They both come to a stop over different lengths of time. The ticker tape patterns for each car are shown on the diagram below.
At what approximate location on the diagram (in terms of dots) does each car begin to experience the impulse?
Which car (A or B) experiences the greatest acceleration? Explain.
Which car (A or B) experiences the greatest change in momentum? Explain.
Which car (A or B) experiences the greatest impulse? Explain.
4. The diagram to the right depicts the before and aftercollision speeds of a car which undergoes a headoncollision with a wall. In Case A, the car bounces off the wall. In Case B, the car crumples up and sticks to the wall.
a. In which case (A or B) is the change in velocity the greatest? Explain.
b. In which case (A or B) is the change in momentum the greatest? Explain.
c. In which case (A or B) is the impulse the greatest? Explain.
d. In which case (A or B) is the force which acts upon the car the greatest (assume contact times are the same in both cases)? Explain.
5. Jennifer, who has a mass of 50.0 kg, is riding at 35.0 m/s in her red sports car when she must suddenly slam on the brakes to avoid hitting a deer crossing the road. She strikes the air bag, which brings her body to a stop in 0.500 s. What average force does the seat belt exert on her?
If Jennifer had not been wearing her seat belt and not had an air bag, then the windshield would have stopped her head in 0.002 s. What average force would the windshield have exerted on her?
6. A hockey player applies an average force of 80.0 N to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced by the hockey puck.
7. If a 5kg object experiences a 10N force for a duration of 0.10second, then what is the momentum change of the object?
Lesson 1: The ImpulseMomentum Change Theorem
 Momentum
 Momentum and Impulse Connection
 RealWorld Applications
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