What causes acceleration? straight line (line of site) path of bullet path of monkey the monkey...
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Transcript of What causes acceleration? straight line (line of site) path of bullet path of monkey the monkey...
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 Acceleration
monkey 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
2
210 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 a
the meaning of “net” force: an object
a forceexertedon theobject
F1F2
F3
4
anotherforceexerted on theobject
IF: 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
NewtonsWsm
kgW
100
1010 2
a 10 kilogram block has a weight on
Earth of 100 N!
1 kg
weight
acceleration = 10 m/s2
NewtonsWsm
kgW
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 balanced
F = 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-Fair
What’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
MassForceNet
onAccelerati
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 Motion
1. 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 Motion
2. 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 Motion
3. 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