Chapter 4

Forces and the Laws of Motion

Changes in Motion

Objectives:1. Describe how force affects the motion of an

object.2. Interpret and construct free-body diagrams.

The Force is Strong With You

● Force is an action exerted on an object which may change the object's state of rest or motion.

● Force may cause a change in an object's velocity with respect to time (acceleration.)

● Forces can cause objects at rest to move, cause objects in motion to stop, and cause objects to change direction.

The Force is Strong With You

● The SI unit of force is the Newton (named for Sir Isaac Newton.)

● The amount of force that, when acting on 1 kg of mass, produces an acceleration of 1 m/s2.

● 1 Newton = 1 kg ▪ 1 m/s2

● Weight is a measure of the gravitational force exerted on an object.

● 1 lb = 4.448 N● 1 N = 0.225 lb

Contact Forces

● Contact forces result from the physical contact between 2 objects.

● Pushing, pulling, throwing, catching

Field Forces

● Field forces do not involve physical contact between objects, rather they are forces that act at a distance.

● Gravitational force, electrical forces (attraction or repulsion)● Masses create gravitational fields in the space around them.● Charged objects create electromagnetic fields in the space

around them.

Field Forces

● All macroscopic contact forces occur as a result of microscopic field forces.

● All contact can be examined on a microscopic atomic level and related to the interactions of atomic particles.

Force Diagrams (Draw a Good Picture!)

● Force is a vector since it has both a magnitude and a direction.

● Force diagrams are diagrams that show force as vectors.● A force vector's tail is attached to the center of gravity of the

object.● A force vector points in the direction of the force and its

length is proportional to the magnitude of the force.

Free-Body Diagrams

● A free-body diagram is a representation of a single object and all the forces acting on that object.

● The forces exerted by the object isolated on other objects are not included in a free-body diagram because they do not affect the motion of the object.

● Free-body diagrams are constructed and analyzed like vector diagrams.

Concept CheckA truck pulls a trailer on a flat stretch of road. The

forces acting on the trailer are the force due to gravity (250 000 N downward), the force exerted

by the road (250 000 N upward), and the force exerted by the cable connecting the trailer to the

truck (20 000 N to the right.) The forces acting on the truck are the force due to gravity (80 000 N

downward), the force exerted by the road (80 000 N) upward, and the force exerted by the car's

engine (26 400 N to the right.) Draw and label free-body diagrams of both the trailer and the

truck.

Newton's First Law

Objectives:1. Explain the relationship between the motion of

an object and the net external force acting on the object.

2. Determine the net external force on an object.3. Calculate the force required to bring an object

into equilibrium.

Inertia

● Inertia is the tendency of an object to resist being moved or, if the object is moving, to resist a change in speed or direction.

● Galileo theorized about the nature of an object to maintain its state of rest or motion.

● Newton furthered Galileo's conclusions by developing Newton's first law of motion– An object at rest remains at rest, and an object in

motion continues in motion with a constant velocity (that is, constant speed in a straight line) unless the object experiences a net external force.

Inertia

● Inertia, therefore, is the tendency of an object not to be accelerated.

● Newton's first law thus states that when the net external force on an object is zero, the object's acceleration (or the change in the object's velocity) is zero.

Net Force

● A car is traveling at a constant velocity.● The net external force on the car is zero.● There are many forces acting on the car (Fforward, Fresistance,

Fgravity, Fnormal)● The individual external forces acting on the car are not zero,

but the net external force is zero.● An external force is a force that acts on an object as a result

of the interaction between the object and its environment.

Net Force

● All four forces acting on the car are external forces.● The net force is the sum of all the forces acting on the car.● Net force is a single force whose external effects on a rigid

body are the same as the effects of several actual forces acting on the body.

● When all external forces acting on an object are known, the net force can be found.

Concept Check

A gust of wind blows an apple from a tree. As the apple falls, the gravitational force on the apple is

2.25 N downward, and the force of the wind on the apple is 1.05 N to the right. Find the magnitude

and direction of the net force on the apple.

Concept Check

2.48 N at 25.0˚counterclockwise from straight down.

Equilibrium

● Equilibrium is the state in which the net force on an object is zero.

● An object that is at rest or moving with a constant velocity is in equilibrium.

● To determine whether an object is in equilibrium, determine the net force.

● If the net force is zero, the object is in equilibrium.● If there is a net force, a second force equal and opposite to

the net force will put the body in equilibrium.

Concept Check

Can an object be in equilibrium if only one force acts on the object?

Concept Check

No. Either no force or two or more forces are required for equilibrium.

Newton's Second and Third Laws

Objectives:1. Describe an object's acceleration in terms of its

mass and the net force acting on it.2. Predict the direction and magnitude of the

acceleration caused by a known net force.3. Identify action-reaction pairs.

Newton's Second Law

● Consider a situation in which you are trying to push a heavy piece of furniture across the room.

● If you try to move it by yourself, the acceleration will be so small it will take a long time to notice a change in velocity.

● If you get your friend to help you, the acceleration will be larger and the furniture will soon be moving very quickly.

Newton's Second Law

● A heavier piece of furniture accelerates less than a lighter piece of furniture.

● It requires less force to accelerated a low-mass object than a high-mass object.

● Newton Second Law– The acceleration of an object is directly proportional

to the net forces acting on the object and inversely proportional to the object's mass.

– ΣF=ma– Net force = mass x acceleration

Concept Check

Space-shuttle astronauts experience accelerations of about 35 m/s2 during takeoff. What force does a

75 kg astronaut experience during an acceleration of this magnitude?

Concept Check

2600 N

Concept Check

An 8.5 kg bowling ball initially at rest is dropped from the top of an 11 m building. The ball hits the ground 1.5 s later. Find the net force acting on the

falling ball.

Concept Check

83 N

Newton's Third Law

● A single isolated force cannot exist.● Forces always exist in pairs.● Newton's third law of motion

– 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.

– For every action, there is an equal and opposite reaction.

Newton's Third Law

● The forces two interacting objects exert on each other form an action-reaction pair.

● The action force is equal in magnitude and opposite in direction from the reaction force.

● Action and reaction forces occur simultaneously.● Action and reaction forces do not cancel each other such

that an object does not move since each force acts on different objects.

Newton's Third Law

● The motion of an object is affected only by the forces acting on that object.

● To determine whether an object will accelerate, draw a free-body diagram of the object and determine whether there is a net force acting on the object.

● Action-reaction forces are equal and opposite, but either object may still have a net force acting on it.

Newton's Third Law and Field Forces

● Newton's third law also applies to field forces.● Consider the gravitational force exerted by the Earth on an

object.● The object will also exert a force on the Earth.● Since the mass of the Earth is greater than the mass of the

object, the acceleration of the Earth towards the object will be negligible when compared with the acceleration of the object towards the Earth.

Everyday Forces

Objectives:1. Explain the difference between mass and weight.2. Find the direction and magnitude of normal

forces.3. Describe air resistance as a form of friction.4. Use coefficients of friction to calculate frictional

force.

Weight

● The weight of an object is calculated by Fg= mag.● Since the acceleration due to gravity (ag) varies with location

of an object in the universe:– Weight is a measure of the gravitational force exerted on

an object; its value can change with the location of the object in the universe.

Normal Force

● The force of gravity is constantly acting on all objects on Earth, since objects are not continuously falling towards the center of the Earth there must be a force opposing the force of gravity to keep them in equilibrium.

● This force is the normal force– A force that acts on a surface that is perpendicular to the

surface.– Normal means perpendicular.

Normal Force

● The normal force is always perpendicular to the contact surface, not necessarily directly opposite the force due to gravity.

● In the absence of other forces, Fn is equal and opposite to the component of Fg that is perpendicular to the contact surface.

● If the angle Θ is the angle between the normal force and the vertical line and also the angle between the contact surface and the horizontal, then Fn = magcosΘ.

Friction

● Static friction is the force that resists the initiation of sliding motion between two surfaces that are in contact and at rest.

● As long as the object does not move, the force of static friction is equal and opposite to the component of the applied force that is parallel to the surface.

● When the applied force is as great as it can be without causing the object to move, the force of static friction has reached its maximum value (Fs,max)

Friction

● Frictional forces occur because of microscopic interactions between contact surfaces.

● When viewed at the microscopic level, surfaces only contact at a few points.

● At these points, surfaces adhere together because of the electrostatic forces between molecules of the two surfaces.

Friction

● Kinetic friction is the force that opposes the movement of two surfaces that are in contact and are sliding over each other.

● Kinetic friction is less that the maximum static friction.● F=Fapplied-Fk

Friction

● Heavier objects require more force to slide across the same surface.

● This is so because the force of friction is proportional to the normal force of a surface on an object.

● Note that the normal force is equal and opposite to the vertical component of the gravitational force of an object on a surface.

Friction

● Friction can be approximated if we know the normal force and Fs,max.

● This is the coefficient of friction– The ratio of the magnitude of the force of friction between

two objects in contact to the magnitude of the normal force with which the objects press against each other.

– μs =Fs, max

– Fn

Concept Check

A 24 kg crate is set into motion on a horizontal floor. Once the crate is in motion, a horizontal

force of 53 N keeps the crate moving with a constant velocity. Find the coefficient of kinetic

friction, between the crate and the floor.

Concept Check

0.22

Concept Check

Two students are sliding a 225 kg sofa at a constant speed across a wood floor. One student pulls with

a force of 225 N at an angle of 13˚ above the horizontal. The other student pushes with a force of 250 N at an angle of 23˚ below the horizontal. What is the coefficient of friction between the sofa

and the floor?

Concept Check

0.25

Air Resistance is a Form of Friction

● Whenever an object moves through a fluid medium, such as air or water, the fluid provides a resistance to the object's motion.

● When the magnitude of the force applied equals the magnitude of air resistance, the net force is zero and the object moves at a constant speed.

● When an object in free-fall accelerates, its velocity increases.

● As the velocity increases, the resistance of the air to the object's motion increases.

Air Resistance is a Form of Friction

● When the upward force of air resistance is equal to the downward gravitational force, the net force is zero and the object moves at a constant velocity.

● The object has reached terminal velocity.

Four Fundamental Forces

● Electromagnetic forces-interactions between protons and neutrons. Acts over long ranges.

● Strong nuclear forces-strongest of the forces.● Weak nuclear forces● Gravitational forces-weakest of the forces. Acts over long

ranges.● All four are field forces.