2. Newton's First Law of Motion

Topic #5. Forces

1. Forces

3. Newton's Second Law of Motion

4. Units of Force

5. Mass and Weight

6. Two Ways to Measure Mass

7. Friction

8. Net Force and Acceleration

9. Free Fall

10. Newton's Third Law of Motion

*11. Forces on Inclined Planes

Notes should include:

Defn: Dynamics is defined as the study of the effects of forces on matter.

Forces: Often a force is described as a push or a pull. Forces are often categorized according to the circumstances where they are observed to occur. For example forces are often categorized as gravitational, electromagnetic, or nuclear, though there are simpler forces such as you, yourself doing something such as pushing down on your desk or bench top. The unit of force is the pound in the British (English) System and is the Newton in the Metric system. The symbol for the pound is “lb” and the symbol for the Newton is N.

Newton's First Law of Motion: In the early 1600's Galileo studied the motion of a ball on an inclined plane. He noticed that as the ball rolled down the ramp due to gravity, the ball's velocity increased at a steady rate. He observed uniform acceleration. He also noticed that when the ball reached the bottom of the incline it moved across the floor with a fairly constant velocity. He figured that on a perfectly smooth floor that went on infinitely the ball would never stop, but roll forever. Galileo concluded that there is a tendency for an object to resist a change in its motion. He gave us the concept of inertia. Inertia is defined as “the tendency for an object to continue in the same motion it has been experiencing right along”. Along came Isaac Newton, who was born the same year that Galileo died. He derived three laws of motion, which were built upon Galileo's work. Newton's First Law of Motion states “an object either remains at rest or in a state of constant velocity if it is not being acted upon by an unbalanced force”. When all forces acting on an object are in a state of balance there is no acceleration. Thus “acceleration is caused by an unbalanced force”. You should know that the net force (symbol FNET) is the sum of all forces acting on an object. When this net force equals zero the sum of all forces acting on an object equals zero. When the net force is NOT equal zero the sum of all forces is equal to a value having a magnitude larger than zero, or not zero. To summarize, if the net force is equal to zero newtons (or pounds), all forces acting upon the object are balanced and there is no acceleration.

Newton's Second Law of Motion: Newton recognized that an unbalanced force is required, if an object is going to experience acceleration. For example, if you push on a piece of furniture with exactly the same amount of effort as someone else who is pushing in the direction opposite to your pushing, the object will not move. To move from rest the object has to experience acceleration. For the object to experience acceleration it has to experience an unbalanced force. The FNET experienced by the object is NOT zero.

Newton's Second Law is often described by the equation F = m a. His second law says that “when an unbalanced force acts on an object, the object will experience acceleration proportional to the size of the unbalanced force”. The direction of the acceleration will be the same as the direction of the force. In this equation F is the net force (FNET), the unbalanced force that causes the acceleration. As the equation shows this force is the product of mass and acceleration.

Units of Force: The unit used to express force measurements is the Newton. It is abbreviated as a capital N. The dimensional analysis of this equation tell us that 1 N = 1 kg m/s2. This means that 1 N of force is equal to a 1 kg mass accelerating at 1 m/s2.

Mass and Weight: Mass measures the amount of matter of which an object is made. Weight is the measure of the force of gravity acting on the object. Weight is a function of position. Though an object’s mass will remain constant regardless of where it is located, the object’s weight is a function of its location, because changing location affects the amount of gravitational force pulling downwards on the object. It is at least theoretically possible for an object to have no weight, that is, a weight of zero pounds or zero newtons, if it were located somewhere far out in space away from any other object of significant mass. Weight is a force that can be expressed in pounds or in newtons. Weight, like all force, is proportional to the acceleration experienced by the object experiencing the force.

If we take Newton's second law and rewrite it for the special case of calculating weight we can write the equation F = m a as W = m g, where g is once again the acceleration due to gravity (9.80 or 9.81 m/s2). At this point you should check to see whether your textbook uses a + g value or a – g value . Some authors prefer to describe downward motion as negative, so the value of g is defined as negative. Other authors prefer to define downwards motion as positive, so the value for g is defined as positive. The outcome of calculations will work out correctly either way, if you are consistent about the sign of all other vector measurements.

Two Ways to Measure Mass: There are two ways to express / determine Mass.

Gravitational Mass: The mass of an object can be found by using a balance which allows you to find the mass of an object by balancing it against known masses, because gravity pulls down equally on both sides of the balance affecting the unknown mass and the matching known masses equally. The balance beam works because the force of gravity is acting "equally" on both sides when the beam is balanced.

Inertial Mass: The mass of an object can also be found by determining the objects "inertial" mass. In this process a known force is applied to the object and its acceleration is determined. From this information the mass is calculated by using the equation F = m a, and solving for a.

Friction: (Air friction is not being discussed here.) Friction is a force. It is the resistance that you observe when you try to slide one object across another. Friction can appear to take various forms, but in all circumstances it involves two surfaces in physical contact moving past each other. This resistance is parallel to the surfaces in contact. Friction is a function of the nature of the two surfaces, which includes how rough the two surfaces are and to what effect weak forces of attraction, such as Vander Waal's forces, have between the two surfaces. When an object is first pulled from rest, it encounters static friction. This kind of friction must be overcome to get the object moving in the first place. On the other hand when an object is being pushed or pulled across a surface the object experiences what is called a sliding friction. Sliding friction is also called kinetic friction. The equation for sliding friction is Ff =  FN. Where  (a Greek letter called mu) is the coefficient of friction and FN is the normal force.

Normal Force: The normal force is perpendicular to the surface an object is on, and results from the surface, itself, pushing against the object. If the object sits on a horizontal surface, the normal force is equal to the magnitude of the object's weight. If the object is on a surface that is inclined such that it makes an angle with the horizontal, the normal force is less than the magnitude of the object’s weight.

Coefficient of Friction: The coefficient of friction is a value between zero and one. Any two surfaces in contact have both a coefficient of static friction (s) and a coefficient of sliding (or kinetic) friction (k). You should expect the coefficient of static friction to always be larger than the coefficient of sliding friction. The coefficient of either type of friction is found experimentally by dividing the force of friction between two surfaces by the normal force "pushing" them together.

NOTE: Friction should not be confused with inertia. It is not the same. Inertia exists with or without the presence of friction.

Free Fall: When an object moves through the atmosphere it experiences air resistance. When an object experiences free fall the object can strike enough air molecules as it falls that it is experiencing an upward force equal to but opposite in direction to the object's weight. At this point the object stops accelerating downwards and continues to move downwards with a constant velocity. This velocity is called a terminal velocity. In a vacuum this could never happen and the object would continue to experience acceleration all the way to the ground. This concept also helps us explain the fact that leaves and pieces of paper do not appear to fall downwards as fast as "heavier" objects such as cinder blocks even though both are being accelerated downwards at the same rate. The difference is due to air resistance. In a vacuum, that is, where there is no air resistance, the leaves and pieces of paper would fall just as fast as the cinder blocks. Of course that doesn't mean that a cinder block landing on you wouldn't hurt more than a single leaf. After all, the cinder block does have a much bigger mass than the leaf and therefore a much bigger force of gravity acting on it than is acting on the leaf. It is that greater force that will give you the headache or worse. Do you think a single leaf hitting you as it free fell in a "no air resistance" environment might hurt more than the same leaf falling from the same height in a normal "air resistance" environment? The answer is yes, it might sting a little, because though it has a low mass it is falling faster than it would in air.

Newton's Third Law of Motion: Often you will hear someone refer to Newton's third law as the law of action and reaction. Newton's Third Law of Motion can be defined as every force is accompanied by an equal but opposite force. No single force acts on a single object. A few examples are:

Two charged objects either attract or repel one another.
Two magnets either attract or repel one another.
You attract the earth due to your mass at the same time the earth attracts you because of its mass.

Forces on Inclined Planes: If you use trigonometry you can deal with forces acting on objects that are positioned on inclined planes. For example, if an object of a certain mass is positioned on a ramp set at a certain angle , both the normal force that presses it against the ramp (it will be less than its own weight because of the incline) and the parallel force that causes it to slide down the ramp can be found by using the cosine of the angle and the sine of the angle respectively. Trigonometry will be studied in the next unit of study, so you can learn to solve problems involving forces in two dimensions.

Vocabulary: Free Body Diagram, Force, Applied Force, Net Force, Force of Friction, Force of Gravity, Weight, Displacement, Position, Velocity (constant, average, instantaneous), Acceleration (constant, average, instantaneous), Air Resistance and Terminal Velocity as well as variable symbols.

Skills to be learned:

Draw Free Body Diagrams

Solve force, acceleration, mass, and weight problems

Solve problems using Newton's Second Law of Motion

Solve Friction Problems using the Coefficient of Friction

Solve Net Force and Acceleration problems (horizontal motion)

Solve Net Force and Acceleration problems (vertical motion)

Assignments:

Textbook: Read / Study / Learn Chapter 6 all sections’ example problems

WB Exercise(s) WB PS# 5-1, 5-2, 5-3, 5-4 and 5-5

Activities: TBA

Resources:

This Handout and the Overhead and Board Notes discussed in class

Text Book Chapter 6

WB Lessons and Problem Sets

- “Study of Forces”

 / Forces