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.