Special theory of relativity Failure of Newtonian mechanics Newton.
9/5/2006PHY 101 Week21 The Laws of Motion …or, Newtonian mechanics.
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Transcript of 9/5/2006PHY 101 Week21 The Laws of Motion …or, Newtonian mechanics.
9/5/2006 PHY 101 Week2 1
The Laws of Motion…or, Newtonian mechanics
9/5/2006 PHY 101 Week2 2
1. The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0.
2. Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma.
3. Action and reaction. For every action there is an equal but opposite reaction.
Newton’s Laws of Motion
9/5/2006 PHY 101 Week2 3
Newton’s second law
9/5/2006 PHY 101 Week2 4
Newton’s second law of motion
F = m a• F = force acting on the moving object, a vector
• m = mass of the moving object
• a = acceleration of the moving object, a vectorIf the force is known, Newton’s second law states how the object (on which the force is acting) accelerates:
m
Fa
What is “force?”
What is “mass?”
9/5/2006 PHY 101 Week2 5
Force and acceleration are vectors.
A vector has both magnitude and direction.
9/5/2006 PHY 101 Week2 6
Three kinds of acceleration
m slows down
m speeds up
m changes direction
9/5/2006 PHY 101 Week2 7
UNIFORM CIRCULAR MOTION
9/5/2006 PHY 101 Week2 8
Example
The “string tension” is the strength of the force exerted by the string at either end.
Centripetal acceleration(Christian Huygens ,1673)
ra ˆ rv2
rmvT
2
rF ˆr
mv2
Therefore, the force on m is
9/5/2006 PHY 101 Week2 9
Analyze free fall including air friction
up) is direction (-
down) is direction (
CF
mgF
Fma
air
gravity
The aerodynamic drag force (C) depends on the size, shape and surface roughness; it is about the same for both balls.
mC
gaCmgma or
• The gravitational acceleration (g) is independent of mass.• Effect of air is inversely proportional to mass:
heavy --- small effect of airlight --- large effect of air
9/5/2006 PHY 101 Week2 10
Newton’s third law
9/5/2006 PHY 101 Week2 11
Which vehicle exerts a greater force ― the tow truck or the car?
9/5/2006 PHY 101 Week2 12
1. The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0.
2. Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma.
3. Action and reaction. For every action there is an equal but opposite reaction.
Newton’s laws of motion
Action means force.
9/5/2006 PHY 101 Week2 13
force on B due to A
force on A due to B
Newton’s third law
We will see than this is very hard to accept! It is just not common sense. That is why it took a great genius like Newton to figure it out.
Whenever one object exerts a force on another object, the second object exerts an equal but opposite force on the first object.
Forces always occur like this, in pairs.
For every action there is an equal but opposite reaction.
9/5/2006 PHY 101 Week2 14
Example – A collision
9/5/2006 PHY 101 Week2 15
Universal Gravitation --- an example of Newton’s third law
ˆ
ˆ
2221
2
1221
1
nF
nF
rmGm
rmGm
9/5/2006 PHY 101 Week2 16
The Earth pulls the apple down (“action”).
The apple pulls the Earth up (“reaction”).
The two forces are equal (but opposite).
9/5/2006 PHY 101 Week2 17
When does a scientific theory become an accepted fact?
9/5/2006 PHY 101 Week2 18
The truck pulls to the right. According to Newton’s third law, the car pulls to the left with an equal force. So how can they start moving, or accelerate?
A puzzle:
Resolution: Consider each part separately, and don’t forget that other forces are also acting.
9/5/2006 PHY 101 Week2 19
Harold Edgerton’s high speed photograph of Wes Kessler kicking a football.
The force exerted by the ball on the toe (reaction) is equal to the force exerted by the toe on the ball.
Really hard to accept!
9/5/2006 PHY 101 Week2 20
MomentumMomentum, , p = mvp = mv
Total momentum is conserved:Total momentum is conserved:
constant. is
law) (third
21
21
2211
22
11
21
00
pppp
vmvmtv
mtv
m
FF
Proof
9/5/2006 PHY 101 Week2 21
The four fundamental forces
• Gravity
• Electromagnetic
• Strong nuclear force •Weak nuclear force
unified by Maxwell’s theory
not really a force, but an interaction that causes certain radioactive decays
comes from QCD, the interaction of quarks and gluons
9/5/2006 PHY 101 Week2 22
FIN
9/5/2006 PHY 101 Week2 23
Newton’s second law and calculus
0
ttv
a
mF
amaF
as
onaccelerati ousInstantane
or
mF
dtdv
differential equation
Isaac Newton invented calculus to solve the equation of motion – to calculate motion for the force that is acting. Generally, calculus is the mathematics that describes continuous change.