Newton – Three Laws of Motion

1. Inertia2. F = ma3. Action = Reaction

Newton’s Laws of Motion

• Law of Inertia: A body continues in state of rest or motion unless acted on by an external force; Mass is a measure of inertia

• Law of Acceleration: For a given mass m, the acceleration is proportional to the force applied

F = m a

• Law of Action equals Reaction: For every action there is an equal and opposite reaction; momemtum (mass x velocity) is conserved

Velocity, Speed, Acceleration

• Velocity implies both speed and direction; speed may be constant but direction could be changing, and hence accelerating

• Acceleration implies change in speed or direction or both

• For example, stone on a string being whirled around at constant speed; direction is constantly changing therefore requires force

Ball Swung around on a String:

Same Speed,(in uniform circular motion)

Changing Direction(swinging around the circle)

Donut Swung around on a String

Force

Acceleration

Conservation of momemtum:action equal reaction

• The momemtum (mv) is conserved before and after an event

• Rocket and ignited gases: M(rocket) x V(rocket) = m(gases) x v(gases)• Two billiard balls: m1 v1 + m2 v2 = m1 v1’ + m2 v2’ v1,v2 – velocities before collision v1’,v2’ – velocities after collision• Example – you and your friend (twice as

heavy) on ice!

Force = (apple’s mass) (acceleration due to gravity)

Equal and OppositeForce from the Table

Net Force is Zero, No Net Motion

Action = Reaction

Acceleration due to gravity• Acceleration is rate of change of velocity, speed or

direction of motion, with time a = v/t• Acceleration due to Earth’s gravity : a g g = 9.8 m per second per second, or 32 ft/sec2

• Speed in free-fall T (sec) v (m/sec) v (ft/sec) 0 0 0 1 9.8 32 2 19.6 64 3 29.4 96 60 mi/hr = 88 ft/sec (between 2 and 3 seconds)

Galileo’s experiment revisited• What is your weight and mass ?• Weight W is the force of gravity acting

on a mass m causing acceleration g• Using F = m a, and the Law of Gravitation

W = m g = G (m MEarth) /R2

(R – Radius of the Earth) The mass m of the falling object cancels

out and does not matter; therefore all objects fall at the same rate or acceleration

g = GM / R2

i.e. constant acceleration due to gravity 9.8 m/sec2

Galileo’s experiment on gravity• Galileo surmised that time differences

between freely falling objects may be too small for human eye to discern

• Therefore he used inclined planes to slow down the acceleration due to gravity and monitor the time more accurately

v

Changing the angle of the incline changes the velocity v

‘g’ on the Moon g(Moon) = G M(Moon) / R(Moon)2

G = 6.67 x 10-11 newton-meter2/kg2

M(Moon) = 7.349 x 1022 Kg R(Moon) = 1738 Km

g (Moon) = 1.62 m/sec/sec About 1/6 of g(Earth); objects on the

Moon fall at a rate six times slower than on the Earth

Escape Velocity and Energy• To escape earth’s gravity an object must have

(kinetic) energy equal to the gravitational (potential) energy of the earth

• Kinetic energy due to motion K.E. = ½ m v2

• Potential energy due to position and force P.E. = G m M(Earth) / R (note the similarity with the Law of Gravitation)• Minimum energy needed for escape: K.E. = P.E. ½ m v2 = G m M / R Note that the mass m cancels out, and• v (esc) = 11 km/sec = 7 mi/sec = 25000 mi/hr The escape velocity is the same for all objects of

mass m

Object in orbit Continuous fall !

Object falls towards the earth at the same rate as the earth curves away from it

Quiz 1• Each quiz sheet has a different 5-digit

symmetric number which must be filled in (as shown on the transparency, but NOT the same one!!!!!)

• Please hand in both the exam and the answer sheets with your name on both

• Question/answer sheets will be handed back on Wednesday after class

• Please remain seated until we begin collecting (20-25 minutes after start)

• Class after quiz