Working through this chapter of the study guide will enable you to:

1. Find out the physical definitions of force and momentum.
2. Understand how changes in the motion of objects correlate with the forces that cause these changes.
3. Learn that the application of forces to objects follows three simple laws formulated by Isaac Newton, and be able to state and explain these laws.
4. Distinguish between weight (a gravitational force) and mass (the quantity of matter), and tell how these are related to each other near the surface of Earth.
5. See that any two massive objects in the universe exert an attractive force on each other.
6. State the conservation laws that apply to linear momentum and angular momentum, and give examples of each.
7. Use proper units when working with the important concepts that you learn about in this chapter.

Discussion

Objects in motion make up a large part of our everyday environment. Even if we can describe and analyze the motion of these objects in detail, we cannot truly understand their motion until we know why the objects move as they do. This means that we must find out what makes things start and stop, that is, accelerate and decelerate. Forces cause all changes in motion, so our next goal will be to learn what forces are and how they affect the motion of objects upon which they act.

In collisions and other interactions between moving objects, studying changes in velocity can teach us a good deal about the behavior of things. The conservation of both linear and angular momentum provides a powerful set of tools for analyzing the interaction of objects with their environment and helps us to explain what we see happening around us. Newton's amazing grasp of the concept of force has opened the door for a complete understanding of the interplay we observe among objects in our daily lives.



Section  3.1Force and Net Force

A force is a quantity that is capable of producing motion or a change in motion—that is, a change in velocity (change in speed or direction), or an acceleration (Chapter 2). A force may act on an object, but its capability to produce a change in motion may be balanced, or canceled, by one or more other forces. The net effect is then zero.

To take into account the application of more than one force, we use the concept of unbalanced, or net, force. Because forces have direction as well as magnitude, they are vector quantities. Forces may act on an object in exactly the same direction, and in that case the net force may be found by adding them. If the forces act in exactly opposite directions, the forces in one direction are subtracted from the forces in the opposite direction, giving the net force.

If the forces act at other angles, the situation is more complicated; graphical or trigonometric analysis must be used. In this textbook, we will not generally deal with such situations.


Section 3.2Newton's First Law of Motion

It may surprise you to learn that no force is required to keep an object moving in a straight line at constant speed, that is, at a constant velocity. Because all objects at Earth's surface are continuously acted on by the force of gravity, and because as soon as objects move they begin to experience a force called friction, it is virtually impossible to observe objects that are not acted on by some applied force. For this reason, it is at first difficult to accept the fact that an object experiencing no forces will continue to move forever at a constant velocity. Galileo discovered this relationship many years ago, and Sir Isaac Newton incorporated the idea into his three laws of motion. Newton's laws are still the basis for our understanding of forces and their effects on the movement of physical objects.

Newton's first law is simply a formal statement of the above idea: An object will remain at rest or in a state of uniform motion unless it is acted on by an external, unbalanced force. This law is used as our working definition of force. As stated in Section 3.1, a force is any quantity capable of producing a change in the motion of an object. Notice that forces may sometimes act on an object and yet not produce a change in its motion if they are properly balanced. Forces that work against one other can cancel each other. When one or more forces that do not cancel are applied to any object, there is an unbalanced force on that object, and some change in its motion must occur.

An additional concept that arises from Newton's first law is that of inertia. Inertia is the property of each massive object that causes it to resist any change in its state of motion. This means that heavy (massive) objects are difficult to start and stop, whereas lighter (less massive) ones can be accelerated easily. Remember that inertia also comes into play when centripetal acceleration is involved. That is, when massive objects are forced to change their direction of motion in order to follow circular paths instead of traveling in straight lines, they resist changes in their motion as well.


Section  3.3Newton's Second Law of Motion

Newton's second law is a quantitative statement of the first law that enables us to calculate the forces and accelerations on massive objects by using numerical data. In words, any unbalanced force will be equal to the mass of the object on which the force acts times the acceleration produced on the object. In its equation form, the second law can be stated in the following way:
F = m a
Using this equation, the rate of change in motion of a massive object (its acceleration) can be determined if the object's mass and the magnitude of the unbalanced force acting on the object is known.

Applying Newton's second law not only allows us to understand why things change their states of motion, but it also shows us how Earth's gravitational pull causes a specific force called weight. The force of gravity produces a nearly constant acceleration (g) on any object located near Earth's surface. Weight (w) can then be determined by multiplying the mass (m) of any object times the acceleration due to gravity (g).
w = m g

Section  3.4Newton's Third Law of Motion

Continuing our discussion of Newton's three laws of motion, we find that his third law shows us how forces always come in pairs. These pairs of forces are always equal in magnitude but opposite in direction. Whenever one object exerts a force on a second object, the second object exerts a force on the first object that is exactly equal in magnitude but opposite in direction. These pairs of forces are often very important in understanding and setting up solutions to problems, so you should get into the habit of identifying them whenever you analyze the forces acting in a given situation. Some good examples in the textbook and in the Study Guide show the application of Newton's third law, so examine both of these presentations carefully. As we study the details of force and its effect on the motion of objects, we begin to better comprehend how physical science explains and predicts events that we experience in our everyday lives. This chapter helps us understand such things as why we fall down when we lose our balance, how dangerous it is to hit a tree or another car when we are driving at a high rate of speed, and why our books slide off the seat when we go around a corner too fast in our car.


Section  3.5Newton's Law of Gravitation

Along with the three laws usually referred to as Newton's laws of motion, Newton developed a relationship describing the interaction of two massive objects with each other. This law states that any two massive objects in the universe (from elementary particles to entire galaxies) are attracted to each other by a force that is directly proportional to the product of their respective masses (m₁ and m₂) and inversely related to the square of the distance (r) between them. Using the universal gravitational constant (G), this concept can be expressed in equation from as:
F = G m₁ m₂ / r ²
The gravitational force defined by this equation is numerically the same as the weight of any object of mass (m) when that object is located at the surface of Earth. Earth's mass (M_E) will then replace m₂ in the above equation, and (r) becomes the radius of Earth (R_E). As long as the object is near Earth's surface, its weight can be calculated using either of the above equations; but if the object is raised to a great height or taken to the surface of some other planet, the universal gravitational equation must be used. Small changes in height are negligible compared with the large radius of Earth, so g remains nearly constant for most of our everyday activities; however, we must be careful to remember that g is not really a constant everywhere throughout the universe, although G is.


Section  3.6Momentum

The remaining two concepts in this chapter help to explain the way that objects in motion interact with each other. These concepts are linear momentum and angular momentum. The power of these ideas lies in the fact that these two forms of momentum are conserved quantities. This means that we can formulate two additional laws to help predict how objects will behave when they interact. Conservation laws deal with quantities in nature that, under certain proscribed circumstances, do not change from one instant to the next. Whenever a given quantity can be counted on to remain the same over a period of time, this fact can be used to calculate the conditions that will exist after certain interactions have taken place.

Momentum is not the only quantity that is conserved. In future chapters, we will learn that energy conservation is also a powerful tool that can help us understand the world around us, but for now we will limit our study to how momentum conservation can be very useful in our understanding of physical science. When momentum does change, it often requires large forces to accomplish these changes, especially if these changes occur over short periods of time. The chapter Highlight should be of special interest, because it shows the reasons behind the successful operation of the air bags in cars and trucks as they apply Newton's laws to make our primary mode of ground transportation safer.

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