Chapter 4 Forces and Newton’s Laws of Motion Why things move the way the do.

Newton’s First Law of Motion “Maintaining the status quo”

Newton’s First Law of Motion “The Law of Inertia” “An object at rest will remain at rest and an object in motion will continue to move at a constant velocity, unless acted upon by a net external force.” The property of an object that causes it to resist changes in its motion is called inertia. Inertia is proportional to an object’s mass. Inertia causes motion at a constant velocity.

Aristotle’s acceptance of a stationary earth…not spinning, was in part due to his lack of a knowledge or understanding of inertia. In the third century BC the Greek philosopher Aristotle developed a model of the structure and motion of the universe. In Aristotle’s world it was assumed that the earth was stationary, did not spin or move through space, and was at the center of the universe.

Newton’s Second Law of Motion “How is Acceleration related to Force?”

Newton’s Second Law of Motion The law of accelerated motion “The acceleration of an object is directly proportional to and in the same direction as the net force acting on it and inversely proportional to the object’s mass.”

Force is a vector and uses the same sign convention as velocity and acceleration.

Summary Constant Velocity Variables:Relationships: Constant Acceleration Variables:Relationships: Caused by Inertia Caused by Net Force

Describing Forces

All forces between objects can be placed into two broad categories: Contact forces Action-at-a-distance forces Contact forces are types of forces in which the two interacting objects are physically contacting each other. Frictional Force Tensional Force Air Resistance Force Spring Force Buoyant Force Action-at-a-distance forces are types of forces in which the two interacting objects are not in physical contact with each other, yet are able to exert a push or pull despite a physical separation. Gravitational Force Electric Force Magnetic Force

Types of Forces Gravitational Force and Weight Friction Fluid Resistance Buoyant Force Normal Force Tension

Newton’s Law of Universal Gravitation: The Gravitational Force “Every mass in the universe exerts a gravitational force on every other mass. The gravitational force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.”

Mass and Weight Mass is a measure of the amount of matter in an object and is related to the object’s inertia. Weight is a measure of the gravitational force acting on an object. The weight of an object equals the product of its mass and the acceleration due to gravity. force of gravity weight, w acceleration due to gravity, g

Comparing the equation for weight with the equation for the gravitational force gives:

The Normal Force When two surfaces are in contact, each surface exerts a force on the other. The component of this force which is perpendicular to the surface is called the normal force, F N.

Friction The force that opposes. Friction is a force whose direction is ALWAYS opposite to the direction an object is moving or would tend to move if there were no friction. Friction is force between two surfaces: 1. the surface of the object and 2. the surface on which it is moving Friction depends on the characteristics of the two surfaces and the force pressing them together.

Static friction exists between a stationary object and the surface on which it rests. Friction depends on whether the object is moving or stationary. Static friction must be overcome before an object can begin moving. Kinetic friction exists between a moving object and the surface on which it is moving. Kinetic friction is always opposite to the object’s velocity. Kinetic friction is usually less than static friction. Static friction is always opposite to the direction the object would move if there was no friction. Static friction equals the net applied force up to its maximum value which depends on the mass of the object and the properties of the two surfaces.

Consider an object sitting on a stationary horizontal surface. If the object remains in contact with the surface, the acceleration in the vertical, y, direction must be zero.

Consider an object sitting on a stationary inclined surface.

If the object remains in contact with the surface, the acceleration in the vertical, y ’, direction must be zero.

The x component of the weight, w x’ tends to cause the object to slide down the incline. The frictional force, f, will be in a direction to oppose this motion. The net force on the object is then:

The acceleration is then:

For an object to begin sliding down an incline:

Tension Force Tension, T, is a “pulling” force applied to an object by wire or rope. Tension always acts along the wire or rope in a direction away from the object on which the tension is applied. When two objects are connected by a wire or rope the tension is the same at each end.

Consider an object with mass m 1 sitting on a table and connected by a wire which passes over a pulley to a second mass m 2 hanging beside the table. Forces Acting on m 1 : Weight = m 1 g Normal Force, F N Tension, T Friction, f Forces Acting on m 2 : Weight = m 2 g Tension, T If released m 2 will tend to fall pulling m 1 to the right.

Newton’s Second Law for m 1 : Y-Direction Assuming object remains on the table. X-Direction Newton’s Second Law for m 2 : Since m 1 and m 2 are connected by a wire the magnitudes of their accelerations must be equal. The directions of the accelerations may not be the same. m 1 tends to accelerate to the right (+) m 2 tends to accelerate down (-)

Substitute a 2 = -a 1

Summary Since m 1 can not accelerate to the left, a 1 > 0, therefore for the system to move m 2 g >  s m 1 g or m 2 >  s m 1

Fluid Resistance Fluid (liquid or gas) resistance is a frictional force that an object experiences as it moves through a fluid (e.g. air or water). Fluid resistance depends on the size and shape of the object, density of the fluid, and is directly proportional to the object’s velocity and in the opposite direction. Example An object falling through air experiences an upward force of air resistance in addition to the downward force of gravity.

Initially air resistance is small because the velocity is small. As the magnitude of the downward velocity increases the force of air resistance increases. Object accelerates downward magnitude of velocity increases If the object falls far enough the force of air resistance becomes equal to the gravitational force.

At this point: This constant velocity reached by an object falling through a fluid is called its terminal velocity.

Buoyant Force An object immersed in a fluid (liquid or gas) experiences an upward buoyant force. The buoyant force depends on the volume of the object immersed in the fluid (volume of fluid displaced) and the density of the fluid. Consider an object dropped into a tank containing a fluid (e.g. oil) Buoyant Force Only Buoyant Force & Fluid Resistance

Buoyant Force with Fluid Resistance The mass of the object is 10kg and the buoyant force is 190N. If the object starts from rest at a height of 63.5m above the surface of the oil how long will it take for it to reach a depth of 60m in the oil? (Ignore any buoyant force due to air and any fluid resistance.)

Part One of the Motion Falling from rest a distance of 63.5m to the surface of the oil. The only force acting on the object is the gravitational force…this part of the motion is Free-Fall. Part Two of the Motion Falling a distance of 60m from the surface of the oil. There are two forces acting on the object: The gravitational force = mg The buoyant force = 190N The object’s velocity as it enters the oil = -35.3m/s

Variables: Relationships: Find t

Substituting values w/o units.

Variables: Relationships: Find t

Substituting values w/o units. Writing in the General Quadratic Form

Simplifying gives:

The time for the object to reach the surface of the oil was 3.6s. Therefore the object is at a depth of 60m in the oil at two times. What is the significance of the two times? What is the maximum depth the object will reach And when does it reach this maximum depth?

Variables: Relationships: Find “d” Find “t”

The object reaches the surface in 3.6s. The object is at a depth of 60m moving downward in 6.2s The object reaches its maximum depth of 67.7m in 7.44s. Time to reach maximum depth: The object is at a depth of 60m moving upward in 8.7s.

Newton’s Third Law of Motion “Forces always come in pairs.”

Newton’s Third Law of Motion “Action and Reaction” “If object A exerts a force on object B, object B must exert an equal and opposite force on object A.” “For every action there is an equal and opposite reaction.” Why do the two forces (action and reaction) not cancel each other? They act on DIFFERENT objects!

Newton’s Third Law says that action and reaction forces are always equal and opposite. It does NOT say that their effects are equal! Consider two objects moving along a horizontal track.