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31-Aug-10 Physics 101
Lecture 4Chapters 3-4
Free FallNewton’s Second Law
Weight & GravityFriction
Quiz Friday -- Chapters 2 & 3
31-Aug-10 Physics 101
Velocity in Free Fall (Up & Down)
Moving upward, with each second the speed decreases by 10 meters/second.
Going back down the motion exactly reverses itself.
See Fig. 3.8 (pg. 43)
Zero m/s10 m/s
20 m/s
30 m/s
40 m/s
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31-Aug-10 Physics 101
Position in Free Fall
How far do objects go when they fall?
More complicated because speed is increasing.
There’s a pattern & Galileo figured it out.
But it wasn’t easy.
5 m
20 m
45 m
Release1 s
2 s
3 s
4 s 80 m
31-Aug-10 Physics 101
Position in Free Fall (cont.)5 meters
20 meters
45 m
Release1 second
2 seconds
3 s
4 seconds80 meters
Distance Fallen =[½ (Acceleration)(Time)](Time)
Galileo realized that:
Gravity acceleration is 10 meters per second per second, so at a time of 3 seconds,
Distance Fallen =½ (10m/s2)(3s)(3s) = 45 m
3
31-Aug-10 Physics 101
Demo: Dropping the Ball
Distance Fallen = d = ½ at2
t2 = 2d/a = 2(3m)/(10 m/s2) = 0.6s2
t = √0.6s2 = 0.77 s
How long does it take a ball to fall 3 meters?Using the formula,
Beauty of science: Predict, then verify by dropping balls!
31-Aug-10 Physics 101
Demo: Catch a Buck
Put thumb and index fingers near Washington’s head. Can you react fast enough to catch the money?
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31-Aug-10 Physics 101
Demo: Reaction Time
Release
Catch
Distance (inch) Time (s)1 0.072 0.103 0.124 0.145 0.166 0.177 0.198 0.2010 0.2312 0.2514 0.2716 0.2918 0.30
31-Aug-10 Physics 101
Force & Acceleration
Newton’s First Law of Motion,
Zero Force Constant Velocity
Definition of Acceleration,
(Acceleration) = (Change in Velocity)
(Time interval)
implies
(same as uniform motion)
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31-Aug-10 Physics 101
Force Implies Acceleration
From those two results we have that,
Net Forcenot Zero
ObjectAccelerates
implies impliesVelocity
notConstant
So, if there’s a net force on an object, the object accelerates.Also, if an object accelerates, there must be a net force on it.
31-Aug-10 Physics 101
Acceleration Goes As Force
Larger the net force, greater the acceleration
Double the Force
Triple the Force
Half the Force
impliesDouble the Acceleration
Triple the Acceleration
Half the Acceleration
implies
implies
Acceleration “goes as” Force Force “goes as” Acceleration.
Mathematically, we write Force ~ Acceleration.
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31-Aug-10 Physics 101
Check YourselfYou push on a crate with 100
Newtons of force. If friction force is 100 Newtons, does the crate accelerate?
Does that mean that crate is not moving?
Now push with 150 N; friction is still 100 N. Does crate accelerate?
A friend helps push with an additional 150 N. By how much does acceleration increase?
31-Aug-10 Physics 101
Mass: Quantity of matter in an objectWeight: Force of gravity on an object
Mass is a universal property.Weight depends on gravity
(different on Moon).
Mass is the measure of inertia.SI unit for mass is the kilogram.SI unit for weight is Newton (since it’s a force)
Mass & Weight
Earth Moon
Weight
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31-Aug-10 Physics 101
More Mass, Less AccelerationThe greater the mass of an object, the less it
accelerates when acted on by same force.
31-Aug-10 Physics 101
Mass & AccelerationFor a given force, greater mass → smaller acceleration
Double the Mass
Triple the Mass
Half the Mass
impliesHalf the Acceleration
Third of the Acceleration
Double the Acceleration
implies
implies
Acceleration goes as the inverse of mass.
Mathematically, we write,Acceleration ~ 1/(Mass).
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31-Aug-10 Physics 101
Check Yourself
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NOFRICTION
31-Aug-10 Physics 101
Newton’s Second Law of Motion
Acceleration goes as net Force.Acceleration goes as inverse of Mass.Acceleration only depends on Force and Mass.
Acceleration is in the direction of the net Force.
(Acceleration) = (Net Force)
(Mass)
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31-Aug-10 Physics 101
Newton’s Second Law of Motion
Or, more familiarly,
, and choosing appropriate units we can make F Fa am m
≈ =
This is the mathematical expression ofNewton’s 2nd Law of Motion.
Units: Mass has SI units of kg, and acceleration has SI units of m/s2. We define the SI unit of force as:1 newton = 1 N = 1kg m/s2.
31-Aug-10 Physics 101
Example: Accelerated Mass
A net force of 3.0 N produces an acceleration magnitude of 2.0 m/s2 on an object of unknown mass.
What is the mass of the object?
1 21
(3.0 N)= 1.5 kg(2.0 m/s )
Fma
= =
m1
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31-Aug-10 Physics 101
Newton’s Second Law of MotionAn object may have several forces acting on
it; the acceleration is due to the net force:
31-Aug-10 Physics 101
Practical Forces• Some contact forces
– Normal Force (Support Force) -- Already discussed– Friction– Drag (Fluid friction)– Spring Force– Tension force (ropes, etc.)
• Some non-contact forces– Gravitational force (Weight)– Electric force
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31-Aug-10 Physics 101
Weight & GravityThe falling box is pulled toward Earth by long-range force of gravity. The gravitational pull on an object on or near the surface of the Earth is called weight, for which we use the symbol W.Weight force is the entire Earth pulling on an object. Weight acts equally on objects at rest or in motion. The weight vector always points vertically downward, and it can be considered to act at the center of mass of the object.
W
W = mg g = 9.80 N/kg = 9.80 m/s2 down
31-Aug-10 Physics 101
Weight on EarthFrom Chap. 3, acceleration of gravity on Earth is about9.8 meters per second per second. (Notation: g = 9.8 m/s2 )
From Newton’s Second Law,
(Force) = (Mass) X (Acceleration)
For example, weight (force of gravity) for 1 kg is
( 9.8 Newtons ) = ( 1 kg ) X ( 9.8 m/s2 )
Can write g as 9.8 N/kg
1kg
9.8 N
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31-Aug-10 Physics 101
Free Fall AccelerationNewton’s Second Law explains why all
objects free fall with same acceleration.
Free Falla = F/m = mg/m = g
1 kg2 kg
a = (1kg)g/(1kg) = g a = (2kg)g/(2kg) = g
31-Aug-10 Physics 101
Newton’s Law of GravityNewton proposed that every object in the universe
attracts every other object with a force having following properties:
1. Force is inversely proportional to square of distance between objects.
2. Force is directly proportional to the product of the masses of the two objects.
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31-Aug-10 Physics 101
Newton’s Law of Gravity
1 21 on 2 2 on 1 2
m mF F Gr
= =
211 26.673 10 N m /kgG −= ×
r is distance between mass m1 and mass m2.
Direction of force on m1 is toward m2; direction of force on m2 is toward m1.
31-Aug-10 Physics 101
Apparent WeightYour perception of your weight is based on the support forces between your body and your surroundings. If your surroundings are accelerating, your apparent weight maybe more or less than your actual weight.
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31-Aug-10 Physics 101
Force felt from contact with the floor (or a scale, etc.) in an accelerating system.
Apparent Weight
Wa> mg
Wa=mg
Elevator accelerates up:
Elevator accelerates down:Wa< mg
Elevator not accelerating:
31-Aug-10 Physics 101
Example: Bowling Ball in a Bag
Carry 6 kg bowling ball in a grocery bag. How much weight does the bag support?
If I yank upwards, accelerating the ball by 5 m/s2, how much additional support force is required?
What is the new total support force?
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31-Aug-10 Physics 101
Support Force of Elevator Cable
Tension in elevator cable depends on acceleration
10 N
1 kg
Zero acceleration
15 N
1 kg
5 m/s2 upward( ½ g upward)
5 N
1 kg
0 N
1 kg
5 m/s2 downward( ½ g downward)
10 m/s2 downward(Free fall)
31-Aug-10 Physics 101
Friction and Air ResistanceFriction and air resistance are forces opposing motion.
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31-Aug-10 Physics 101
FrictionOrigin of friction is molecular interaction between
solid surfaces.
Friction is complicated.
Friction depends on support force and on properties of the surface.
Basic properties of friction first established by Leonardo da Vinci.
31-Aug-10 Physics 101
Air Resistance (Drag)Origin of drag is molecules of gas (or liquid) striking
a moving object.Drag force depends on:
•Size (area) of the object•Speed of the object
Larger the size or speed, larger the drag.Also depends on shape of object, density of gas or liquid, etc.
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31-Aug-10 Physics 101
Air Resistance on a Falling ObjectGravity force on an object (i.e., weight) is constant but air resistance depends on an object’s speed.
As a falling object gains speed, the resistance force gets larger so the net force decreases.
Net force is sum of:Weight (downward)Resistance force (upward)
31-Aug-10 Physics 101
Check YourselfGolf ball has more mass than a ping-pong
ball. Force of gravity is greater on: golf ball, ping-pong ball, or the same?
The two balls are the same size; when speeds are equal, drag force is greater on which ball?
Which ball falls faster (which has greater acceleration)?
GolfBall
PingpongBall
Drag
Weight
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31-Aug-10 Physics 101
Terminal SpeedSpeed of falling objects increases until drag force
balances weight. When forces balance, zero acceleration so constant velocity.
Speed for which air resistance balances weight called terminal speed.
High terminal speed
Low terminal speed(large area of chute)
31-Aug-10 Physics 101
Key Points of Lecture 4
Before next lecture, read Hewitt through Chap. 4, into 5
Homework Assignment #1 (first graded assignment) is due before 11:00 PM on Thursday, Sept. 2.
Homework Assignment #2 (second graded assignment) is due before 11:00 PM on Sunday, Sept. 5.
Quiz Friday (Chaps. 2 & 3)
• Velocity changes in free fall: v = gt• Position change in free fall: d = ½gt2
• Newton’s Second Law: a = F/m or F = ma• Weight• Gravitational Force• Apparent Weight• Friction• Air drag and terminal speed