Momentum Two factors are necessary to describe an

Momentum • Two factors are necessary to describe an objects “tendency” to stay in motion. q mass. q velocity

Momentum • We call the measured “tendency” of an object to remain in motion momentum. • We define momentum, symbolized as p, as the product of mass and velocity. Øp = m v (reference tables)

Practice Problem • An object whose mass is 4. 5 kilograms is traveling at 20 m/s [east]. Calculate the momentum of the object. • What are the units of momentum?

Momentum and Impulse • “Momentum” is a commonly used term in sports. • An object (or team) with momentum is going to be hard to stop.

Momentum and Impulse • To stop an object with momentum, it is necessary to apply a force against its motion for a given period of time. • 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.

Momentum and Impulse • The concepts in the previous slide should not seem like abstract information to you. You have observed this a number of times if you have watched the sport of football.

Momentum and Impulse • 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 stop the car's momentum. • An object with momentum can be stopped if a force is applied against it for a given amount of time.

Momentum and Impulse • Put another way, an unbalanced force always accelerates an object – either speeding it up or slowing it down. • The concept of momentum, then, is merely an outgrowth of Newton’s 2 nd Law!

Momentum and Impulse • Newton’s 2 nd Law: Ø Fnet = m a • Can be written as: Ø Fnet = m * (Δv / t) • We can then rewrite Newton’s 2 nd Law in the following form: ØFnet * t = m * Δv

Momentum and Impulse • Fnet * t = m * Δv = Δp • We call the quantity F * t the impulse delivered to the object. • Impulse is symbolized by the letter J • Units of impulse are the Newton • second are equivalent to the unit kg • meter per second

Momentum and Impulse • J = F*t = m*Δv = Δp (reference tables) • From Newton’s 2 nd Law it follows that the impulse delivered to the object changes its momentum • So… this equation really says that Impulse = Change in Momentum

Practice Problem • A 5. 0 kg object traveling at 3. 0 meters per second [east] is subjected to a force that increases its velocity to 7. 0 meters per second [east]. Calculate: • • • a) the initial momentum of the object b) the final momentum of the object c) the change in momentum of the object d) the impulse delivered to the object e) if the force acts for 0. 20 seconds, what are its magnitude and direction?

Conservation of Momentum • Consider a collision between two objects – object 1 and object 2. • Assume that the two objects are not subjected to any net external forces (this is called a closed system).

Conservation of Momentum • In such a collision, the forces acting between the two objects are equal in magnitude, but opposite in direction (Newton’s 3 rd Law) F 1 = -F 2

Conservation of Momentum • The forces act between the two objects for a given amount of time. Regardless of how long the time is, it can be said that the time that the force acts upon object 1 is equal to the time that the force acts upon object 2. t 1 = t 2

Conservation of Momentum • It follows then that… F 1*t 1 = -F 2 * t 2 • Since F*t = Δp = m * Δv, it follows that… m 1 * Δv 1 = -m 2 * Δv 2

Conservation of Momentum • A little more manipulating of this equation… m 1 v 1, f - m 1 v 1, i = - (m 2 v 2, f – m 2 v 2, i) • Which gives… m 1 v 1, i + m 2 v 2, i = m 1 v 1, f + m 2 v 2, f • And finally… pbefore = pafter (Reference Tables)

Conservation of Momentum • pbefore = pafter is an expression of the Law of Conservation of Momentum

Conservation of Momentum • The Law of Conservation of Momentum is especially useful when applied to collisions. • The momentum lost by one object is equal to the momentum gained by another object.

Conservation of Momentum

Let’s Practice • A 5. 0 kg gun fires a 0. 0020 kg bullet. If the bullet exits the gun at 800 m/s [east], what is the recoil velocity of the gun?

Let’s Practice Some More • Review Book Page 236 #50 & 51 (June ‘ 04 Exam) • Review Book Page 271 #72 (June ‘ 03 Exam)

Myths In The Movies

The Mighty Ducks Challenge Question In terms of impulse and momentum, why does the egg break some times, and not break other times?

Real-world Applications • The effect of collision time upon the amount of force an object experiences. • The effect of rebounding upon the velocity change and hence the amount of force an object experiences.

Effect of Collision Time • Consider an object flying thru the air that has 100 kg m / s of momentum, and it is about to collide with something, bringing it to rest. • The greater the time over which the collision occurs, the smaller the force acting upon the object. 200 N x 0. 5 sec = 100 kg m / s 100 N x 1 sec = 100 kg m / s 50 N x 2 sec = 100 kg m / s 25 N x 4 sec = 100 kg m / s

Effect of Collision Time • Thus, to minimize the effect of the force on an object involved in a collision, the time must be increased; and to maximize the effect of the force on an object involved in a collision, the time must be decreased. • There are several real-world applications of this phenomena…. .

Effect of Collision Time Boxers “ride the punch” to extend the time of impact of the glove with their head, thus minimizing the effect of the force in the collision.

Effect of Collision Time Rock climbers. Nylon ropes used have some stretch. The stretch extends the time the force is applied to the climber in the event of a fall, thus reducing the force.

• "Teaching should be such that what is offered is perceived as a valuable gift and not as a hard duty. ” • Albert Einstein

Effect of Collision Time • Demonstrations Egg Toss Water Balloon Toss

The Effect of Rebounding • Occasionally when objects collide, they bounce off each other (as opposed to sticking to each other and traveling with the same speed after the collision). • Bouncing off each other is known as rebounding.

The Effect of Rebounding involves a change in direction of an object; the before- and after-collision direction is different.

The Effect of Rebounding • If cars rebound, there is a larger impulse applied to the car. • Automobiles are made with crumple zones. • By crumpling the car is less likely to rebound. • By crumpling, the collision time is also extended.