Forces and the Laws of MotionForces and the Laws of Motion

Force, Mass, and AccelerationForce, Mass, and Acceleration

PVHS PhysicsPVHS Physics

Objectives

Students should be able to analyze situations in which a particle remains at rest, or moves with constant velocity, under the influence of several forces.

Students should understand the relation between the force that acts on an object and the resulting change in the object’s velocity

Students should understand how Newton’s Second Law, , applies to an object subject to forces such as gravity, the pull of strings, or contact forces

Students should be able to analyze situations in which an object moves with specified acceleration under the influence of one or more forces

Students should understand the significance of the coefficient of friction

Students should understand the effect of drag forces on the motion of an object

Students should be able to apply Newton’s Third Law in analyzing the force of contact between two objects that accelerate together

A little review…

What is acceleration? What causes

acceleration? What are the types of

forces?

What we know…

Inertia… Is an object’s

resistance to a change in motion

it is the tendency of an object to maintain its state of motion

Mass is a measure of inertia More mass… more

inertia Less mass… less

inertia

What we know… The Law of Inertia …

“An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force”.

Net Force… The vector sum of all

the external forces acting on an object

What we know…

Forces are Vectors Equilibrium…

The state in which there is no change in an object’s motion

The sum of all forces equals zero

0F

What we know… Finding the Net Force…

List givens and draw a free-body diagram

Establish x-y axes (frame of reference)

Resolve vector components

Sum the vectors in each direction

NNNF

F

x

y

21113

0

What happens when the Net Force is not zero?

Forces and Motion

Forces cause an object’s velocity to change… Since acceleration is the rate of change in

velocity… Force causes acceleration

The acceleration is directly proportional to the force The bigger the force, the greater the acceleration The smaller the force, the smaller the acceleration

Fa

or,

Forceonaccelerati

FF

Mass and Motion

Inertia… Is an object’s resistance to a change in motion Inertia resists acceleration Mass is a measure of inertia

Acceleration in inversely proportional to mass More mass, less acceleration Less mass, greater acceleration

ma

or,mass

1onaccelerati

1

m

m

Force, Mass, and Motion

Combining the effects of mass and force…

This is Newton’s Second Law

mF

a

,ormassForce

onaccelerati

,thenmass

onaccelerati,Forceonaccelerati

1

mF

a

,ormassForce

onaccelerati

,thenmass

onaccelerati,Forceonaccelerati

1

Newton’s Second Law

“The acceleration of an object as produced by a net force is directly proportional to the magnitude of the force, in the same direction of the force, and inversely proportional to the mass of the object”

The 2nd Law is commonly written as:

F=ma “The sum of the forces on an object equals mass

times acceleration” Note: it is the Net Force that causes the acceleration

Application…

The net force on the propeller of a 3.5kg model airplane is 7.0N. What is its acceleration?

A 2.0kg otter starts from rest at the top of an incline 85 cm long and slides to the bottom in 0.50s. What is the net force on the otter?

Who is pushing who?

Newton’s Third Law

“For every action, there is an equal and opposite reaction” … Newton’s 3rd Law

Forces always exist in pairs called Action-Reaction Pairs When two objects interact they exert forces on

one another that are equal and opposite This includes field forces and physical forces

Action-Reaction Pairs don’t cancel Each force acts on a different object…

This law explains why both cars are dented in a car accident. (Can you think of any other examples of Newton’s Third Law?)

Newton’s Third Law

Newton’s Third Law

Lets Talk about Friction… Friction always resists motion Two types of Friction

Static… no motion/ stationary and forces in equilibrium

Kinetic… object in motion, forces may or may not be in equilibrium

Static friction force is greater than Kinetic friction force

Friction

Do you think friction forces vary with the type of surface?

Do heavy objects have more friction than lighter objects? Why?

Friction

Normal Force… the force perpendicular to the contact surface between two objects

W

Normal Force (N)

W

Normal Force (N)

Friction

Friction is proportional to the normal force

normal

friction

normalfriction

F

F

,or

FF

normal

friction

normalfriction

F

F

,or

FF

is the is the coefficient of frictioncoefficient of friction and depends on and depends on the type of surfacethe type of surface

Friction Typical Typical coefficients of frictioncoefficients of friction… depends on the type of … depends on the type of

surface surface

Coefficient of Friction

Surfaces Static Friction Kinetic Friction

Steel on steel (dry) 0.6 0.4

Steel on steel (greasy)

0.1 0.05

Teflon on steel 0.041 0.04

Brake lining on cast iron

0.4 0.3

Rubber tires on dry pavement

0.9 0.8

Metal on ice 0.022 0.02

Rubber tip of crutch on rough wood

0.7  -

Newton’s Laws and Friction

Useful Equations…

Net force: F = ma (units… newtons = kg m/s2)

Gravitational force: W = mg

Frictional force: Ffriction = Fnormal

An applied force of 50 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance.)                                

Practice #1

An applied force of 20 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the coefficient of friction (µ) between the object and the surface, the mass, and the acceleration of the object. (Neglect air resistance.)

Practice #2

A 5-kg object is sliding to the right and encountering a friction force which slows it down. The coefficient of friction (µ) between the object and the surface is 0.1. Determine the force of gravity, the normal force, the force of friction, the net force, and the acceleration. (Neglect air resistance.)

Practice #3

Practice #4

Demo… A 2.0 kg block accelerates down a 35 degree ramp. If it travels 2.0 m in 4 seconds, what is the coefficient of friction?

Practice #4

Do… A 1.0 kg block slides down a down a 30 degree ramp with a coefficient of friction of .15. How long will it take to slide 2.0m?

What about Air Resistance?

Air Resistance is a friction force

In general, Air Resistance (aka Drag) is proportional to velocity or the square of velocity

etc... shape, area, surface density, fluid, of on type depend B andA

2or BvFAvF dragdrag

What is Terminal Velocity?

As an object falls through a fluid, its velocity and Drag (air resistance) increases

At a certain velocity, the drag equals the force of gravity and the object stops accelerating… equilibrium is reached and the net force is zero

When equilibrium is reached the object has attained Terminal Velocity

B

mgv

A

mgvmgAv

mgAvF

T

TT

T

2 v Drag if similarly,

or,

0

Velocity, Terminalat

Air Resistance and Terminal Velocity

Create qualitative x-t, v-t and a-t graphs of a falling object with air resistance…

What we know…

How does force affect the motion of an object? How do free-body diagrams help in analyzing forces

and motion? What are Newton’s Laws of Motion? How can you determine forces required for

equilibrium? How is mass related to motion? What are action-reaction pairs and why don’t they

produce equilibrium? What is the difference between mass and weight? What is a normal force? How can you determine the force due to friction?

Questions?