Forces and the Laws of Motion

Chapter 4

Forces and the Laws of Motion4.1 Changes in Motion

– Forces• are pushes or pullss• can cause acceleration.• are measured in newtons (N).

– 1 N = 1 kg.m/s2

• can act through contact or at a distance.– Contact forces occur when objects touch.– Field forces occur when objects do not touch.

» electric fields» magnetic fields» gravitational fields

• are vectors and are drawn with arrows.

Forces and the Laws of Motion• Types of Contact Forces

– Applied Force, Fapp: An applied force is a force exerted on an object by a person or an object or an action which directly pushes or pulls on the object. - pushing a box across the floor

– Spring Force, Fspring, is the force exerted on an object by a compressed or stretched spring.

Forces and the Laws of Motion• Types of Contact Forces

– Friction Force, Ffrict: The friction force opposes the applied force and is exerted by a surface on an object it moves across or makes an effort to move across the surface. Air resistance, Fair is a friction force.

– When pushing a box across the floor, the surface of the floor exerts friction on the object.

– Tribology is defined as the science of interacting surfaces in relative motion

Forces and the Laws of Motion• Types of Contact Forces

– Tension Force, Ftens or FT: This is the force exerted by a rope, cable, or string, when it is attached to an object and pulled taut. It is directed away from the object and along the rope at the point of attachment.

Forces and the Laws of Motion• Types of Contact Forces

– Normal Force, Fnorm or Fn or FN : The normal force is a support force that acts on a surface in a direction perpendicular to the surface.

Forces and the Laws of Motion• Gravity (Weight)

Fg or W or mg: On Earth the force of gravity is often referred to as the weight of an object. It is the attractive force of the earth. And is always directed toward the center of the earth. It has a magnitude equal to the mass of the object times the acceleration due to gravity, or mg.

Forces and the Laws of Motion4.1 Force Diagrams show force vectors as arrows.

1. Identify the object or system.2. Identify the forces acting on the object and the direction of the forces. 2. Draw a diagram (a dot or box) to represent the isolated object.3. Draw and label vector arrows for all external forces acting on the object.

A free body diagram is a diagram showing all of the external forces acting on an object (not showing forces exerted by the object in question on other objects!).

Free body diagrams are used to determine the vector sum of all the forces acting on an object.

• Steps for drawing a force diagram:• Identify the object you will draw a diagram for.  (If there are multiple objects of interest, you will need to draw

multiple diagrams.) • Identify all the forces acting directly on the object and the object exerting them.  With the exception of gravity and

certain other forces rarely used in first semester physics (magnetism, electric force), the two objects will be in direct contact.  Do not include forces by an object acting through another object--only include the force due to the intermediate object.

• Draw a dot to represent the object of interest. • Draw a vector to represent each force.  Draw it in the direction the force is being exerted, and label it by (a) the

type of force, (b) the object exerting the force, and (c) the object receiving the force (which will be you object of interest).  It will have the form F(type)exerting object -> object of interest

• If the object is stationary or is moving at a constant velocity, the vectors should graphically add up to zero.  If the object is accelerating, the sum of the vectors should produce a vector in the same direction as the acceleration.

• Writing down the sum of the forces• Identify direction of every force and of acceleration. • Pick a coordinate system to minimize the number of things (forces and acceleration) that must be broken into

components, especially unknown values • Draw the components for any forces or acceleration that does not lie along the X or Y axis, and identify the angle

that is given (or being looked for). • Pick one direction and write down all the forces or components of forces in that direction, using positive and

negative signs to identify those in the positive and negative directions. • Set the sum of the forces in that direction as equal to the mass multiplied by the acceleration in that direction.  (If

not moving or moving at a constant velocity in that direction, acceleration will be zero.) • Repeat for the other direction.

• Vector Review– The resultant vector is the sum of two or more vectors and can

be determined trigonometrically or graphically.– A single vector can be resolved into two or more components

that have the same effect.

Forces and the Laws of Motion

FFx = F.cos

Fy = F.sin

– Concurrent forces act through the same point at the same time and can be combined to find the resultant vector.

Forces and the Laws of Motion4.2 Newton’s First Law – The Law of Inertia

An object at rest remains at rest, and an object in motion continues in motion with constant velocity (that is, the same speed and the same direction) unless acted upon by an unbalanced force or net external force.

Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. (Galileo 1630’s)

An object maintains constant velocity until acted upon by a net force.

When the net external force on an object is zero, the object does not accelerate.

4.2 Newton’s First Law – The law of 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.

– Inertia is the tendency of an object not to accelerate.

– Mass is a measure of inertia. – Mass is the amount of matter in an object.– Inertia is directly proportional to mass. The

greater mass an object has then the greater the inertia of that object.

– car and wall– truck and ladder

Forces and the Laws of Motion

Forces and the Laws of Motion4.2 Newton’s First Law – The law of Inertia

(Fnet = 0)

Forces and the Laws of Motion4.2 Determining Net Force

Net force is the vector sum of forces acting on an object.

Fx = Fforward – Ffriction = 0

Fy =Flift - Fgravity = 0

Fforward

Fgravity

Flift

Ffriction

Fnet = 0 N

4.2 Determining Net ForceForces and the Laws of Motion

35oFg

FnFfrict

35o

35o= 35o

55o

Fg.sin

Fg.cos

Coordinate System:

X-axis is parallel to the slope.

Y-axis is perpendicular to the slope.

4.2 Determining Net Force1. Define the problem.2. Select a coordinate system, and apply it to the free-

body diagram. (Make the x-axis parallel to the incline and the y-axis perpendicular to it.)

3. Find the x and y components of all vectors.4. Find the net force in both the x and y directions.

(Sum the forces in the x direction and sum the forces in the y direction.

5. Find the net force. If there is a net force in both the x and y directions, use vector addition (Pythagorean theorem) to find the total (or single) net force on the object.

Forces and the Laws of Motion

• 4.2 Equilibrium– Equilibrium is the state in which the net force

on an object is zero. – Objects at rest or at constant velocity are in

equilibrium. – When there is a net force acting on an object,

the equilibrant force is the single force that if applied to an object would produce equilibrium.

Forces and the Laws of Motion

Forces and the Laws of Motion

Forces and the Laws of Motion

Forces and the Laws of Motion

Forces and the Laws of Motion

• Practice – p. 128 1-3– p. 129 1-5

Forces and the Laws of Motion• 4.3 Newton’s Second Law of Motion

– According to Newton’s first law when a net force does act on an object its motion changes, that is, it accelerates.

– The Law of AccelerationThe acceleration of an object is directly proportional to the net

force acting on an object and inversely proportional to the object’s mass.

F = ma a = F/mm = F/a

F = ma or net force = mass x acceleration

Forces and the Laws of MotionWhat do we know about acceleration?

Acceleration is the rate of change in velocity.Acceleration occurs when an object speeds up, slows down, or

changes direction (at constant speed or changing speed).a = v/t = (vf-vi)/t

Acceleration is zero if velocity is constant.vf = vi + at

When acceleration is constant:x = vit + ½ at2

vf = vi + 2ax2 2

Forces and the Laws of Motion• 4.3 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 force there exists an equal in size and opposite in direction reaction force.

– Forces always exist in pairs.– Action and reaction forces are two forces that act on

two different objects.– Field forces also exist in pairs. The earth exerts a

force of gravity on you and you exert a force of gravity on the earth.

– Practice with handout.

Forces and the Laws of Motion• 4.4 Everyday Forces

– Weight• magnitude of the gravitational force exerted on an object• scalar• depends on location • Fg = mag = mg = m.9.81 m/s2 on Earth• The greater the distance between Earth and the object

the less weight the object has.– The Normal Force

• normal means perpendicular• is the support force perpendicular to an object and the

surface it touches

Forces and the Laws of Motion• 4.4 Everyday Forces

– Friction• Friction opposes the applied force.• Static friction opposes the initiation of motion between two

surfaces in contact and at rest.

• Fs = - Fapp until Fs = Fs,max and a greater Fapp will cause motion.

• Kinetic friction, Fk, is the retarding force on an object in motion.

Fnet = Fapp – Fk

• Kinetic friction is less than static friction.

Forces and the Laws of Motion• 4.4 Everyday Forces

– Friction• Friction results from complex interactions between

contacting surfaces which include electrostatic forces between the molecules and atoms.

• The force of friction, Ff, is proportional to the normal force.• The force of friction between two surfaces is

approximately equal to the normal force multiplied by the coefficient of friction for the two surfaces. Ff = Fn

The coefficient of friction is a ratio of forces.

k = Fk/Fn

s = Fs,max/Fn

The coefficient of friction is a ratio of forces.

k = Fk/Fn

s = Fs,max/Fn

Forces and the Laws of Motion• 4.4 Air Resistance, FR

• a form of fluid friction• FR increases with

increasing speed.

Forces and the Laws of Motion• 4.4 Four Fundamental Forces

Unified Field Theory