Newtons Second Law of Motion Force and Acceleration.
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Transcript of Newtons Second Law of Motion Force and Acceleration.
Newton’s Second Law of Motion
Force and Acceleration
Movement
When we see something move we seeStartSlowCurveStop
All these things represent a CHANGE in motion
Formulas to remember
Acceleration = change in velocity
time interval
What is the cause of acceleration?FORCE
Force causes Acceleration
Example – hockey puck in iceStill until force is placed on itStays moving in a straight path until another
force causes it to accelerate Change directionSpeed upSlow down
Change in velocity acceleration
Net force causes acceleration
Combination of force yields accelerationDouble the force – double the
accelerationMathematically –
Acceleration ~ net force “~” means “directly proportional to”
Mass resists acceleration
ExampleFull shopping cart vs. empty shopping cartThe greater the mass the more force it
takes to accelerate the objectAcceleration is inversely proportional to
massAcceleration ~ 1
mass
As the denominator increased the wholequantity decreases
Newton’s Second Law
The acceleration produced by the force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force and is inversely proportional to the mass of the object
Mathematically: acceleration~ net force mass
Applications of 2nd Law
Using consistent units
a = F
ma =acceleration
(m/sec^2 )F = force
(newtons)m = mass (kg)
Acceleration – which way?
Net force action on an object and its resulting acceleration are always in the same direction
The spool demo:Which way will it roll?Does it change from top to
bottom?
Problem Solving
One Newton – the force needed to give a mass of one kilogram an acceleration of one meter per second per second.1 N = (1 kg) (1 m/sec/sec)1 N = 1 kg m/ sec^2
If we know two quantities, we can solve for the third
Problem 1
How much force, or thrust, must a 30,000-kg jet plane develop to achieve an acceleration of 1.5 m/sec^2
F = ma
= (30,000 kg)(1.5 m/sec^2) = 45,000 kg m/sec^2
= 45,000 N
Problem 2
What acceleration is produced by a force of 2000 N applied to a 1000-kg car?
a = F/m = 2000 N/ 1000 kg = 2000 kg m/sec^2/1000 kg = 2 m/sec^2
If the force is 4000 N, the acceleration doubles 4000N/1000 kg = 4 m/sec^2
Questions
If a car accelerates at 2 m/sec^2, what acceleration can it attain if it is towing another car of equal mass?
Answer – the same force on twice the mass produces half the acceleration or
1 m/sec^2
Questions
What kind of motion does a constant force produce on an object of fixed mass?
A constant force produces motion at a constant acceleration, in accordance with Newton’s second law.
Friction
Is a forceMust be in contactDirection opposite
to motionForce is needed to
overcome frictionCaused by
irregular surface
Extent of friction
Depends on kinds of material
How much surface are pressed together
ExamplesRubber on concreteSteel on steelGuard rails are now
concrete instead of steel
Friction in Fluids
Fluids – liquids and gases Caused by object trying to move
particles apart in order to pass thru it Try to run in water?
Liquid friction can be quite high Air resistance – notice at high
speeds Biking or skiing
Friction and Force
When friction is present, object may only move at a constant speed even if you apply force (instead of accelerating)
The net force is zero
PUSH
FRICTION
Air Resistance
Weight
Questions
Two forces act on a book resting on a table: its weight and the support force from the table. Does a force of friction act as well?
No, not unless the book tends to slide. Friction only acts when there is motion
Question
Suppose a high-flying jet cruises with a constant velocity when the thrust from its engines is a constant 80,000 N. What is the acceleration of the jet? What is the force of air resistance acting on the jet?
Answer
The acceleration must be zero because the velocity is constant. Since the acceleration is zero, if follows a = F/m the net force is zero. This means the force of air resistance is 80,000 N and it acts in the direction opposite to the jet’s motion.
Applying Force - Pressure
No matter how you place a book on a table, the force is the sameTry varying the way it is placed on a
scaleHowever – place a book on your
palm or on top of a pencil which goes into your hand……PRESSURE – has to do with force and
area
Pressure
The amount of force per unit areaPressure = force
area of applicationP = F
A P=pressure (pascals) F= force (newtons) A = area (meter^2)
1 Pascal = 1 N/m^2
Pressure comparisons
Pressure on your footTwo feetOne footPointe (ballerina)
Calculating the pressure on your foot with graph paper
Bed of Nails Questions
In attempting to do a bed of nails, would it be wise to begin with a few nails and work upward to more nails?
No, no, no! There would be less physics teachers with fewer nails. The resulting greater pressure would cause harm.
Bed of Nails question
The massiveness of the cement block plays an important role in this demo. Which provides more safety, a small block or a more massive block?
The greater the mass, the smaller the acceleration of the block and the bed of nails towards the friend. Much of the force from the hammer goes into breaking the block. The block must be BIG and must BREAK!
Free Fall explained
Galileo did his famous experiment off the leaning tower of Pisa.Dropped a 10 kg cannon
ballDropped a 1 kg stone at
same timeResult – accelerations are
equalBut why?
Newton’s law
F = maTherefore a = F/m
If an item is large it has a large force and a large mass
If an item is small, it has a small force and a small mass
Either way the RATIOS are the same
F/m = F/m
Galileo's experiment
a = F/m = 9.8 N/ 1 kg rock = 9.8 m/sec^2a = F/m = 98 N/10 kg cannon ball= 9.8 m/sec^2
Question – if you were on the moon an dropped a hammer and a feather at the same time, would they strike the surface of the moon at the same time?
Answer
Yes. Astronaut David Scott did this exact experiment on the moon. They both accelerated at 1/6 g.
Falling and Air resistance
Example – feather and coin in a tube.With air – coin falls rapidly, the feather
flutters downWithout air – both reach the bottom at the
same time
feathercoin
weight
Air resistance
Terminal Speed or Velocity
Speed during freefall, when the air resistance on the object equals the weight of the falling object.Terminal speeds of various objects
Feather – 5 m/secCoin – 200 km/hrSkydiver – 150 – 200 km/hParachute – 15-25 km/h
Question
If a heavy person and a light person open their parachutes together at the same altitude and each wears the same size parachute, who will reach the ground first?
The heavy person. Light person reaches terminal speed first and it will be slower than terminal speed for the heavy person.