Newton – Three Laws of Motion

1. Newton – Three Laws of Motion • Inertia • F = ma • Action = Reaction

2. 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

3. 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

4. Ball Swung around on a String: Same Speed, (in uniform circular motion) Changing Direction (swinging around the circle)

5. Acceleration Force Donut Swung around on a String

6. 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!

7. Force = (apple’s mass)  (acceleration due to gravity) Action = Reaction Equal and Opposite Force from the Table Net Force is Zero, No Net Motion

8. 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)

9. 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

10. 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

11. ‘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

13. 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

14. Object in orbit  Continuous fall ! Object falls towards the earth at the same rate as the earth curves away from it

17. 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