Chapter 4

Forces and the Laws of Motion

Chapter Objectives

• Define force

• Identify different classes of forces

• Free Body Diagrams

• Newton’s Laws of Motion

• Define Equilibrium

• Identify different types of everyday forces

Definition of Force

• Force is defined as the cause of acceleration.

• We often think of it as a push or a pull on some object.

• Force causes a change in velocity.

• That could mean magnitude and/or direction.

Contact v Field Forces

• The first class of force that we will talk about is contact.

• A contact force is a force that arises from the physical contact of two objects.

• This would include such forces as a bat striking a baseball, a receiver catching a football, friction, etc.

• The second class of force that we will talk about is field.

• A field force is a force that can exist between objects, even in the absence of physical contact between the objects.

• This would include such forces as gravity, magnetism, static electricity, etc.

Free Body Diagrams

• Because force deals with acceleration, and acceleration is a vector quantity, therefore force is a vector.

• To show the forces acting on an object we draw a free body diagram.

• A free body diagram is a diagram of an object showing all forces acting on that object.

• Free body diagrams are drawn of objects as they are isolated from the rest of the objects in the system.

Things to Remember in a Free Body Diagram

1. All forces originate from the center of mass of the object.

2. The vector to represent the force of gravity always points straight down.

3. The vector to represent the force of friction always opposes applied force.

4. When an object is in contact with a surface, there is a normal force that is directed perpendicular to the surface.

Fn

Fa

Fg

Ff

Newton’s First Law

• An object at rest remains at rest, and an object in motion continues in motion with constant velocity (that is constant speed in a straight line) unless the object experiences a net external force.

• We will shrink that down to say objects in motion tend to stay in motion unless acted upon by an outside force.

• This is also called the Law of Inertia.

• Inertia is the tendency of an object to resist acceleration.

Newton’s Second Law

• The acceleration of an object is directly proportional to the net external force acting on the object and inversely proportional to the object’s mass.

• We will take that mess and shrink it down to one simple formula:

• This will become our standard formula for calculating force in this book.

• Force is measured in Newtons (N).– Which is 1 kg x m/s2

F = ma

Newton’s Third Law

• If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction.

• We will shrink that tongue twister down to for every action, there is an equal and opposite reaction.

• Notice that the action-reaction is done by two different objects.

• Example: You are pushing down on your chair and the chair is pushing up on you.

Equilibrium

• Equilibrium is defined as the state in which there is no change in the body’s motion.

• Based on Newton’s First Law, equilibrium is achieved when the net external force on an object is equal to 0.– This is known as the 1st

Condition for Equilibrium

• That means that the acceleration of the object is 0.– Which means the velocity of

the object is constant.

• Constant as in at rest, or constant as in moving at a constant velocity.

Weight

• Weight is the name given to the magnitude of the force of gravity acting on an object.

• Weight can change based on the acceleration due to gravity.

• Since the acceleration due to gravity on Earth is assumed to be constant, weight is constant on Earth.

• Weight would be less on the moon since the acceleration due to gravity on the moon is less. (About 1/6 that of earth.)

F = ma Fg = mg

Normal Force

• Remember that the normal force is the force exerted on an object perpendicular to the surface of contact.

• So this force exists when there is an object sitting on a table, floor, ground, or an inclined plane.

• If the object is sitting on a level surface, then the normal force is equal but opposite to the force of gravity, or weight of the object.

• If it is not on a level surface, then you need to break the force of gravity vector down into components.

Fn

Fg

Fn

Fg Θ

Inclined Plane

Fn

Fg Θ

If we flip the force of gravity vector and take advantage of a trigonometry proof, we see that the angle between the normal force and the force of gravity is equal to the angle of the incline.

Θ

Using trig properties, we can calculate Fn by using the cosine function of Θ.

Fn = Fgcos Θ

Facts About Friction

• Friction opposes the motion of an object, and the motion is created by the applied force. – So friction opposes the applied force.

• The force of friction is proportional to the normal force.

• Friction depends on the surfaces in contact.

• The characteristics of the surfaces are taken into account by assigning a coefficient of friction to the surfaces in contact.

• The coefficient of friction is represented by the Greek letter “mu”…μ.

Air Resistance• Air resistance (FR), or (Fair), is the resistive force that

opposes relative motion of an object as it flows through the fluid medium of air.

• This is based on the surface area of an object, the density of the fluid, and the speed at which the object is traveling through the fluid.

• At low speeds, the air resistance is roughly proportional to the car’s speed.

• At high speeds, the air resistance is roughly proportional to the square of the car’s speed.

• When the magnitude of FR is equal to the applied force, that is when an object reaches terminal velocity.

Types of Friction• Static friction is the resistive

force that opposes relative motion of two contacting surfaces that at rest with respect to one another.

• This is measured with the least amount of force necessary to make an object move.

• Static friction is always greater than kinetic friction.

• You will need to know the coefficient of static friction.

• Kinetic friction is the resistive force that opposes the relative motion of two contacting surfaces that are moving past one another.

• This is measured as the least amount of force necessary to keep an object moving at constant velocity.

• Static friction is always greater than kinetic friction.

• You will need to know the coefficient of kinetic friction.

Fs = μs Fn Fk = μk Fn

Tension

• Tension is nothing more than the force exerted in a string, spring, rope, etc.

• Symbolized as FT or just T.

– The tension vector is always drawn away from the object.

– If there is a string connecting two objects, the tension is directed away from both of them.

FT

T1

T2