Basic Physics. Isaac Newton ( ) Topics. Newton s Laws of Motion (2) Newton s Laws of Motion (1) PHYS 1411 Introduction to Astronomy

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1 PHYS 1411 Introduction to Astronomy Basic Physics Chapter 5 Topics Newton s Laws Mass and Weight Work, Energy and Conservation of Energy Rotation, Angular velocity and acceleration Centripetal Force Angular Momentum Universal Law of Gravity Isaac Newton ( ) Building on the results of Galileo and Kepler Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler Major achievements: 1. Invented Calculus as a necessary tool to solve mathematical problems related to motion 2. Discovered the three laws of motion 3. Discovered the universal law of mutual gravitation Newton s Laws of Motion (1) 1. A body continues at rest or in uniform motion in a straight line unless acted upon by some net force. An astronaut floating in space will continue to float forever in a straight line unless some external force is accelerating him/her. Newton s Laws of Motion (2) 2. The acceleration a of a body is inversely proportional to its mass m, directly proportional to the net force F, and in the same direction as the net force. a = F/m F = m a 1

2 Newton s Second Law of Motion Newton s Laws of Motion (3) 3. To every action, there is an equal and opposite reaction. The same force that is accelerating the boy forward, is accelerating the skateboard backward. m = 1 kg M = 70 kg V =? v = 7 m/s Newton s Third Law of Motion What is Newton s Third Law (law of action and reaction)? How to find the Weight on Earth? Weight is a Force = mass x acceleration due to gravity Weight in Newtons = mass in kg x 9.8 m/s 2 for Earth Mass is a property of matter, it is not equal to weight Apple (m) Earth (M) Weight of apple = mg = m x 9.8 m/s 2 = F g Video 1 Video 2 Newton's Laws of Motion 2

3 Work and Energy Work Work = Force x distance SI units: Newton's x meter = Joules Example: A 1 kg object at a height of 1 m from ground experience a force of 9.8 N, when it falls to the ground it does work that is W = 9.8 N x 1 m = 9.8 N.m = 9.8 J Work and Energy Energy Ability of a body to do work Work due to motion is called Kinetic Energy (KE) KE = ½ x mass x velocity 2 measured in Joules Example: If a 1 kg object fall from a height of 1 m with a velocity of 4.43 m/s KE = ½ x 1kg x (1 m/s) 2 = 9.8 J Work and Energy Gravitation Potential Energy Work due to Gravity is called Gravitational Potential Energy (GPE) measured in Joules GPE = mass x g x h (h = height with respect to a reference point) If a 1 kg object falls from a height of 1 m, its GPE is GPE = 1kg x 9.8m/s 2 x 1m = 9.8 J Fundamental Law of Nature Conservation of Energy In all the three examples above we find that Work = KE = GPE Energy can neither be created or destroyed: It only transforms from one form to the other. Example: Dropping a ball converts GPE to KE and at impact KE to heat, sound and work Work and Energy This is called conservation of energy. Energy is transformed from gravitational to kinetic and to heat, sound and mechanical Power Power Rate at which energy is expended Power (P) = Work / time = Joules /seconds = watts (w) 3

4 Conservation of Energy Demo Conservation of Energy and Kepler's Second Law of Planetary Motion Mindcraftwounderhowto.com Things that Move in Circles: Units Radian: An angle at the center of a circle whose arc is equal in length to the radius Units of Measure: Radian, Degrees and Revolutions 1 radian = 57.3 degrees Source: wikipedia Things that Move in Circles Angular velocity (ω) = change in angle / change in time rad/s or rev/s, or deg/s Angular Acceleration (α) = change in ω / change in time rad/s 2 or rev/s 2, or deg/s 2 Newton s Second Law for Rotating Bodies Any object that moves in a circle or an arc has centripetal force Centripetal force (F c ) measured in Newton s F c = ma = m v 2 / r Centripetal (radial) acceleration a c = v 2 / r Circumference = 2 π r v = 2 π r / t r v Source: share.ehs.uen.org Source: faculty.wcas.northwestern.edu 4

5 Visual Demo of Centripetal Force Consequences of Centripetal Force Why planets are not perfect spheres? Image source: NASA, STSI Solar System Source: Wikipedia Galaxy Angular Momentum Rotating and or orbiting object poses angular momentum Angular Momentum is Conserved I is called Moment of Inertia ~ MR 2 M is mass and R is radius of disk Source: wikipedia Newton s Law of Gravitation Any two bodies are attracting each other through gravitation, with a force (F g ) proportional to the product of their masses (M,m) and inversely proportional to the square of their distance (r). G is called gravitational constant. F g = GMm r 2 Gravity and Distance: The Inverse- Square Law Inverse-square law -- relates the intensity of an effect to the inversesquare of the distance from the cause in equation form: intensity = 1/distance 2 for increases in distance, there is decreases in force even at great distances, force approaches but never reaches zero YouTube 5

6 Inverse-Square Law Force of Gravity and Inverse-Square Law Gravitational Constant How to find the value of G? G=6.67x10-11 N.m 2 /kg 2 How to find g of a Planet? Weight = Gravitational Force F g = Gm 1m 2 d 2 Apple (m) Earth (M) Gravitational force is significant only for very large masses and small separation distance If we know G, M and r then we can find g How to find the mass of Earth? Weight = Gravitational Force mg = GMm r 2 M = g r 2 G Apple (m) Earth (M) Since g, r and G are known we can calculate the mass of Earth = 6 x kg 6

7 Acknowledgment The slides in this lecture is for Tarleton: PHYS1411/PHYS1403 class use only Images and text material have been borrowed from various sources with appropriate citations in the slides, including PowerPoint slides from Seeds/Backman text that has been adopted for class. 7