NEWTONS LAW OF MOTION

Newton's third law - Giancoli, Ch 4, section 5 visit the Physics Classroom for this topic
1. State Newton's third law of motion.
· Newton's third law of motion describes how objects (more than one) interact with one another
· According to Newton, "For every action there is an equal and opposite reaction". This means that when two bodies A and B interact, the force that A exerts on B is equal and opposite to the force that B exerts on A.
· The interaction can be through contact -- like in a collision -- or at a distance -- like the earth and the moon. Regardless of the objects involved -- mass makes no difference here -- the two objects will exert equal forces on each other. The bug hits the windshield with the same force that the windshield hits the bug.
· While the forces are equal, the effect of the force (because of mass -- here it does matter) may be very different. Combining the second and third laws allows us to say: mA = Ma
2. Discuss examples of Newton's third law.
· In order to walk you must exert a force on the ground that is directed backwards. The reaction of the ground is to push you forward.
· The horse and cart
· Rockets lifting off -- the rocket pushes the exhaust particles out and the exhaust particles push the rocket

Inertial Mass, Gravitational Mass and Weight - Giancoli, Ch33, p. 948
3. Define inertial mass.
· Inertial mass is the mass that is present in Newton's second law of motion (Fnet = ma). Therefore, the definition of inertial mass is as follows: mi = Fnet / a. In words, inertial mass is the ratio of net force to acceleration.
4. Compare gravitational mass and inertial mass.
· Gravitational mass is the mass of an object that describes how it "feels" the gravitational force exerted by other masses. Near the earth, this mass is the mass responsible for the weight of an object. The definition of gravitational mass is as follows: mg = W / g
· While the concepts of inertial mass and gravitational mass arise from different areas of physics, they are mathematically equivalent. No experiment has been able to distinguish between the two.
· Consider the simple example of a mass in free fall near the surface of the earth. The only force acting on the object is the gravitational force (its weight). According to Newton's second law of motion, we may set Fnet = W. But, W = mgg and Fnet = mia. Therefore, we may state: mgg = mia. Finally, this means that the acceleration of an object in freefall, a, is given by the relation: a = (mg / mI) g. According to Galileo, all objects fall at the same rate of acceleration. This is only true if the ratio mg / mi has a value of 1. In other words, mg = mi.
5. Discuss the concept of weight.
· Weight, by definition, is the net gravitational force exerted on an object. W = mg
· Weight is typically measured using a support scale (like the bathroom scale you have at home). In most cases, the bathroom scale will report the true weight (defined as mg) of an object. This will be true as long as the scale and object are experiencing static or translational equilibrium -- neither is accelerating.
· In non-equilibrium cases, for example a support scale used in an accelerating elevator, the value given by the scale will reflect the motion of the object and will not report the "true weight" (= mg) of the object. The "apparent weight" of an object on a rising elevator will be greater than its true weight. The "apparent weight" of an object on a descending elevator will be less than its true weight.
6. Distinguish between mass and weight.
· Mass is a measure of the amount of matter contained within an object. We have seen that it can be inertial or gravitational in nature (#4 above). Mass is a fundamental property of matter and does not change with location.
· Weight is a specific force involving the concept of gravitational mass. Weight depends greatly on location and will change if the object is moved to a different location.

Momentum - Giancoli, Ch 7, all sections visit the Physics Classroom for this topic
7. Define linear momentum and impulse.
· Linear momentum is defined as the product of mass and velocity. p = mv
· Newton's second law of motion can be written as follows: F = ma = mDv / Dt = m(vf - vo) / Dt = (mvf - mvo) / Dt
Or, F = Dp / Dt. That is, the net force acting describes the rate at which its momentum changes.
· We can define a new quantity, impulse, which describes how momentum changes. From Newton's second law of motion, we see that Dp = F Dt. Impulse is calculated as F Dt. The result of the impulse is to change the momentum by an amount = Dp.
· Large forces acting over small time intervals produce the same impulse as small forces over large time intervals.

8. State the law of conservation of linear momentum.
· We will define a system of objects to contain all objects that will interact with one another.
· External forces are defined as forces that are exerted from outside the system of objects.
· Internal forces are defined s forces that are exerted by the objects within the system of objects.
· In the absence of external forces (an isolated system), the linear momentum of a system of objects is conserved. It can be neither created nor destroyed. It may, during the course of interactions between objects in the system, be transferred from one object to another.
v1
v1f
v2
v2f9. Derive the law of conservation of momentum for an isolated system consisting of two interacting particles.
The two objects in the diagram will interact. The result of the interaction is that each object will acquire a different final velocity. While they are interacting, Newton's third law of motion applies. Newton's second law describes the result for each object.

During the interaction: F1 = - F2 b/c of Newton's third law
We can write: Dp1 / Dt = - Dp2 / Dt b/c of Newton's second law
We can write: Dp1 = - Dp2 b/c Dt is the same for both objects
This means: p1f - p1o = - (p2f - p2o)
Simplify: p1f - p1o = -p2f + p2o
Rearrange: p1f + p2f = p1o + p2o
(p1 + p2)f = (p1 + p2)o
Group: pf = po Total momentum is conserved!

10. Solve problems involving momentum and impulse.
· Regardless of the type of collision involved, linear momentum for an isolated system (no external forces) is conserved.
· If external forces are present, then the momentum will change according to the impulse relation.
· It might sometimes be useful to classify collisions between objects by the way that energy is distributed in the collision. Those collisions for which kinetic energy is conserved are called elastic collisions. If the kinetic energy is not conserved, but is transformed into other types of energy then the collision is called an inelastic collision.
· To apply momentum conservation, calculate the individual momentum of each object (remembering that momentum is a vector quantity) prior to the collision and add them to find the initial momentum of the system. Similarly, find the individual momentum of each object after the collision and add them to find the final momentum of the system. Then, set the initial vector momentum of the system equal to the final vector momentum of the system.


PROBLEMS - Giancoli, Ch 7 #3, 5, 9, 15, 19, 21, 25, 32, 39, 42, 63, 71