# Newton’s Second Law of Motion

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Newton’s Second Law of Motion
Force and Acceleration

Movement When we see something move we see
Start Slow Curve Stop 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 ice Still until force is placed on it Stays moving in a straight path until another force causes it to accelerate Change direction Speed up Slow down Change in velocity  acceleration

Net force causes acceleration
Combination of force yields acceleration Double the force – double the acceleration Mathematically – Acceleration ~ net force “~” means “directly proportional to”

Mass resists acceleration
Example Full shopping cart vs. empty shopping cart The greater the mass the more force it takes to accelerate the object Acceleration is inversely proportional to mass Acceleration ~ mass As the denominator increased the whole quantity 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 m a =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 force Must be in contact Direction opposite to motion
Force is needed to overcome friction Caused by irregular surface

Extent of friction Depends on kinds of material
How much surface are pressed together Examples Rubber on concrete Steel on steel Guard 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 Free-body diagrams
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 Air Resistance Free-body diagrams PUSH Weight FRICTION

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 same Try varying the way it is placed on a scale However – 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 area Pressure = force
area of application P = F A P=pressure (pascals) F= force (newtons) A = area (meter^2) 1 Pascal = 1 N/m^2

Pressure comparisons Pressure on your foot
Two feet One foot Pointe (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 ball Dropped a 1 kg stone at same time Result – accelerations are equal But why?

Newton’s law F = ma Therefore 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^2
a = 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 down Without air – both reach the bottom at the same time Air resistance feather coin weight

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/sec Coin – 200 km/hr Skydiver – 150 – 200 km/h Parachute – 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.

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