What causes acceleration?

straight line(line of site)

path ofbullet

path of monkey

the monkey begins to fall ad theprecise moment when the ballleaves the barrel of the gun

The ball and themonkey arrive atthe point markedby the reddot at thesame time

What causes acceleration?

AnalysisFirst, imagine what would happen in the absence of gravity

Object External Influence Motionmonkey none “floats” in placeball none straight line with constant speed

Result: ball hits monkey

Object External Influence Motionmonkey gravity uniform acceleration toward groundball gravity sideways at constant speed + downward

with uniform acceleration

Result: ball hits monkey

It’s very useful to consider motion without the effects of gravity!

What causes acceleration?

Aristotle: forces cause velocities Galileo: “external influences” Newton: “unbalanced force”

For now we define force according to its effect on the motions of things-the operational definition we find is concisely expressed by three (3) simple rules

First we examine how forces act – then we look at a restatement of the rules

Preliminary Issue: mass, weight and what they mean to freely falling monkeys

Mass1. a measure of how much matter is in an object.. literally

proportional to the number and size of atoms in the object

2. a measure of the internal resistance of an object to a change in its motion…perhaps you could think of it as a measure of the objects “desire” to remain in motion at a constant speed in a straight line.

What causes acceleration?

Mass* mass is an intrinsic property of an object – to change the mass of anone must make a change (physical, chemical, or nuclear) in the object

* in order to make two objects accelerate at the same rate one must pull or push harder on the more massive object

In the monkey demonstration (and in Galileo’s law of falling) we observe thatobjects under the influence of gravity alone fall with equivalent rates of acceleration

object External Influence Accelerationmonkey force of gravity (weight of monkey) 10 m/s2

ball force of gravity (weight of ball) 10 m/s2

grain of sand weight of grain of sand 10 m/s2

dump truck weight of dump truck 10 m/s2

let’s look at this…………….

What causes acceleration?object resistance to acceleration External Influence Accelerationmonkey mass of monkey weight of monkey 10 m/s2

ball mass of ball weight of ball 10 m/s2

grain of sand mass of grain of sand weight of grain of sand 10 m/s2

dump truck mass of dump truck weight of dump truck 10 m/s2

amount of stuff external influence on the stuff

acceleration ofthe stuff(the motionalreaction)

• Conclusion: There must be a direct proportionality between weight and mass

more mass greater influenceof weight force

but, sameacceleration!!

What causes acceleration?

By analyzing free-fall we conclude that:

AND that the weight force is proportional to the mass:

onacceleratimassForce

massweight

mass

weight

twice as muchmass

twice as muchweight

massweight

massweight

sm

2210 2

sameratio

What causes acceleration?The genius of Newton and the power of explanation

Newton: gravity is only one type of force (what about friction, pushingpulling, electric attraction or repulsion…)gravity is “special” in the sense that gravitational force (a.k.a. weight) isproportional to mass

Nevertheless, whenever any net force acts upon any mass to cause anyacceleration, the rule is:

NET FORCE = MASS X ACCELERATION

F = m athe meaning of “net” force: an object

a forceexertedon theobject

F1F2

F3

4

anotherforceexerted on theobjectIF: acceleration

(F3 = F4) F2 > F1 to the right(F3 = F4) F1 > F2 to the left(F3 = F4) F1 = F2 none (i.e. straight line at constant speed)

NOW YOU TRY!!

Net ForceWhen forces balance, there is equilibrium.

F1 = Force felt by Bo because of Diddley.

F2 = Force felt by Diddley because of Bo.

F1 = F2

F1 F2

Bo Diddley

What causes acceleration?Force is a vector quantity!

TOTALNET FORCE

ON AN OBJECT

MASSOF THEOBJECT

ACCELERATIONOF OBJECT CAUSED

BY NET FORCE= X

expressed in“Newton's”

[N]

expressed in“kilograms”

[kg]

expressed in“meters per second, per

second”m/s2

F1 F2

mass say F1 > F2 then

(F1 – F2) = mass x acceleration = ma

acceleration for F1 > F2

What causes acceleration?

The “Newton” is the standard measure of force in the system we use.

Push on a 1 kilogram MASS with a FORCE of 1 Newton then the object willACELLERATE at a rate of 1 m/s2 in the direction of the force….provided thatthe force is not “balanced” by another force on the object.

If your body contains 75 kg of massthen…

on earth you weigh (force) about 75kg X 10 m/s2 = 750 Newtons

mass acceleration

Some examples

1. Mass and weight(a) in free-fall on Earth

10 kg

weight

acceleration = 10 m/s2

net force = mass X acceleration

NewtonsWsmkgW

100

1010 2

a 10 kilogram block has a weight on

Earth of 100 N!

1 kgweight

acceleration = 10 m/s2

NewtonsWsmkgW

10

101 2

1 kg weighs 10 Newtons on EarthConvert to lbs= 1 kg weighs about 2.2 lbs

2. sitting on a table on Earth

What forces are acting on the apple?

W = weight force exerted by theEarth on the apple

F = contact force exertedby table on the block

Net forceupward mass acceleration= X

F – W = 1 kg X 0 m/s2

F – W = 0 Newtons

for the acceleration to be equal to zero the forces must be balancedF = W = 1 Newton

1 kg

If two forces act in opposite directions, the net force is in the direction of the larger force and is equal to the difference between the larger and smaller force

3. skydiving

10 kg

W = weight force exerted byEarth ON block

Fair = force of air resistance exerted BY air on block

acceleration

If Fair = 60 Newtons at what rate does the block accelerate?

1. First find the “NET FORCE” : W-FairWhat’s the weight? W = mass X g = 10 kg X 10 m/s2 = 100 NNET FORCE = 100 N – 60 N = 40 N

2. NET FORCE = MASS X ACCELERATION 40 N = 10 kg X ACCELERATION

3. Solve for acceleration:

241040

sm

kgN

MassForceNetonAccelerati

Terminal velocity – The speed at which air resistance (aka drag) matches thepull of gravity,resulting in a constant fall rate.

What is the net force on a skydiver as she falls at terminal speed?

NET FORCE = MASS x ACCELERATION

Fait – W = M x AFait – W = M x 0 = 0Fait – W = 0

What is the force of air resistance on a skydiver whose mass is 40 kilograms whenshe falls at terminal speed?

NET FORCE = ZEROFait – W = 0Fair = W = 40kg X 10 m/s2

40 kg

W = weight force exerted byEarth ON block

Fair = force of air resistance exerted BY air on block

acceleration = 0

Laws of Motion1. Newton’s 1st Law: An object at rest, remains at rest, OR if in motion, travels in a straight line at constant velocity, UNLESS acted on by a net force.

Laws of Motion2. Newton’s 2nd Law: For a body having constant mass, M, the NET

FORCE APPLIED to the body, the Mass of the body, and the observed Acceleration of the body are related by:

FORCE = MASS X ACCELERATIONF = MA

A 2 kg mass is acted on by a 2 N force. What is its acceleration? a = 2 N / 2 kg = 1 m/s2

What if a 0.5 N frictional force was also in place?a = (2 - 0.5 N)/2 kg

= 0.75 m/s2

2 kgF = 2N

2 kgF = 2N f = 0.5 N

Laws of Motion3. Newton’s 3rd Law: For every action there is an equal and opposite

reaction. – rule of force pairs

• Objects can not act on one another without being acted upon.• When you strike a wall, does it hurt your hand? You might say the

wall struck you. Newton would say the force you applied to the wall was the same as that which the wall applied to you. The wall is bigger and more massive, therefore has more inertia and was not harmed as much as you.

Weight

AppliedForce“Pushing”

frictional forcefrom wallReaction

force from wall

If you push on a wall, the wall pushesback on you. It does so with a forceequal in strength to the one you exert on it!

The “rule of force pears”

For every force exerted ON an object, the object exerts an equal andoppositely directed force ON its environment

Force on Rock from Earth = Force on Earth from Ball

a = F/m = g Rock acceleration

a = F/m Earth’s acceleration

Gravity

Gravity

contact force exertedby table on the apple contact force

exerted by theapple on the table

force of Earth onthe apple

force of appleon the Earth