3. Impulse Newton’s second law of motion, F = ma, can be rewritten by using the definition of acceleration as the change in velocity divided by the time needed to make that change. It can be represented by the following equation

4. Multiplying both sides of the equation by the time interval, Δt, results in the following equation:

5. The right side of the equation, mΔv, involves the change in velocity: Δv = v f – v i. Therefore, mΔv = mv f – mv i. The product of the object’s mass, m, and the object’s velocity, v, is defined as the momentum of the object.

6. Momentum is measured in kgm/s. An object’s momentum, also known as linear momentum, is represented by the following equation. Momentum is a VECTOR quantity – that means we must describe it with a number telling us how BIG it is (we call that “magnitude”), AND a number telling us the direction the object which has this momentum is moving.

7. This will then give us the “Impulse Momentum Theory” or… FΔt = Δp

12. Momentum in a Closed, Isolated System Under what conditions is the momentum of the system of two balls conserved? The first and most obvious condition is that no balls are lost and no balls are gained. Such a system, which does not gain or lose mass, is said to be a closed system. The second condition required to conserve the momentum of a system is that the forces involved are internal forces; that is, there are no forces acting on the system caused by objects outside of it.

16. Let’s do a problem on the board… A 35.0-g bullet moving at 475 m/s strikes a 2.5-kg bag of flour that is on ice, at rest. The bullet passes through the bag, as shown in Figure 9-7, and exits it at 275 m/s. How fast is the bag moving when the bullet exits?

17. Nearly 400 years ago, Johannes Kepler observed that comet tails appeared to be blown by a solar breeze. He suggested that ships would be able to travel in space with sails designed to catch this breeze. Thus, the idea for solar sails was born.

18. How Does a Solar Sail Work? A solar sail is a spacecraft without an engine. A solar sail works like a giant fabric mirror that is free to move. Solar sails usually are made of 5-micron-thick alu­minized polyester film or polyimide film with a 100-nm-thick alu­minum layer deposited on one side to form the reflective surface. ( By the way... a micron, short for micrometer, is a unit of measurement equal to one millionth of a meter. A micron is actually 0.000039 of an inch.)

19. Reflected sunlight, rather than rocket fuel, provides the force. Sunlight is made up of individual particles called photons. Photons have momentum, and when a photon bounces off a solar sail, it trans­ fers its momentum to the sail, which propels the spacecraft along. The force of impacting photons is small in comparison to the force rocket fuel can supply. So, small sails experience only a small amount of force from sunlight, while larger sails experi­ence a greater force. Thus, solar sails may be a kilometer or so across. Photons supplied by the Sun are constant. They impact the sail every second of every hour of every day during a space flight. The Sun’s continuous supply of photons over time allows the sail to build up huge velocities and enables the spacecraft to travel great distances within a convenient time frame. Rockets require enor­mous amounts of fuel to move large masses,