PHYS 1403 Introduction to Astronomy Gravity Chapter 5 Announcement Exam 1 February 21 st 2018 2:25pm 3:40 pm during class time Chapter 1,2,3,4 and 5 40 Multiple Questions. One short answer essay type question. Bring a green Scantron sheet, No. 2 pencil and a scientific calculator. No cell phones allowed. You can bring one page US letter size reference sheet with equations, constants or conversion factors only. Review questions will be on class web page on or after February 15 th. Topics in Chapter 5 Speed, Velocity and Acceleration, Momentum Law of Falling Body Newton s Laws Work, Energy and Power Circular Motion Orbits and Gravity Einstein and Relativity Topics for Today Speed, Velocity and Acceleration, Momentum Law of Falling Body Newton s Laws a v Motion Motion is one of the most necessary functions of all living things. Exactly what is motion and what law s govern its behavior has been the most crucial question ever since man began to reason. 1
Speed Speed: The most simple definition is called speed. S=distance/time S / Example A friend takes 2.0 hours to drive from his house in Stephenville to DFW airport at an average speed of 65 mi/h. How far is the airport from the friends house. Answer: 130 mi v / Velocity SI units of velocity are meters/second (m/s) Velocity (v): For speed we did not put any importance to the direction of motion. The friend would travel the same distance from DFW to Stephenville. When we associate direction with a number then the speed changes its name from speed to velocity. Physical Quantities in Physics and Astronomy In physics many physical quantities have direction in addition to magnitude (number). Example speed is a physical quantity that just has a number but velocity is a physical quantity that has a direction and a number. How do we handle the arithmetic of physical quantities that have both number and a direction. We define Vectors and Scalars Vectors and Scalars Any physical quantity that has only magnitude is called a scalar. We can just use the normal arithmetic rules. Any physical quantity that has a magnitude and direction is called a vector. We cannot just use the normal arithmetic rules. We have to consider how to take care of directions. Examples of Scalars: Speed (s), Distance (d) Work (W), Energy (E) etc. Examples of Vectors: Velocity (v), Acceleration (a), Force (F), Momentum (p), Torque (τ), Angular Momentum (L) We use arrows, the length of the arrow gives the magnitude of velocity and the arrow head direction How is velocity different from speed? Example : A runner makes one lap around a 200 m track in a time of 25 seconds. What is the runner s average speed and average velocity. Velocity is with respect to reference point whereas speed is not. How is velocity different from speed? v v v Moon F Earth Speed = 200/25 = 8 m/s Velocity = 0/25 = 0 m/s 2
What happens when velocity changes with times? Acceleration (a): We define a quantity called acceleration (a). acceleration ( m /s 2 ) = change in velocity (m/s) / time interval (s) a v/ t i.e. how fast is velocity changing. A very common experience is when you step on a car s accelerator. Acceleration depends on Mass Inertia Mass is a intrinsic property of matter Mass provides resistance to motion Inertia is a measure of resistance to motion Momentum If two vehicles move with the constant but different velocity hit a wall, which vehicle will cause the most damage? Galileo s Observations of Motion The acceleration of a freely falling body due to force of gravity is independent of the mass (weight), or shape of the falling object Momentum = Mass x Velocity SI units of momentum is kg.m/s 3
Galileo and the Law of Falling Body Galileo found that the speed of the falling object increases (acceleration) by 9.8 m/s after every second Galileo called this acceleration due to gravity of Earth g = 9.8 m/s 2 The distance the object drops in meters from its starting point is 4.9 Law of Falling Body A ball is dropped from the top of a building, How far has it dropped in meters after 2 seconds D = 4.9t 2 D = 4.9 x 2 x 2 = 19.6 meters Acceleration due to Gravity (g) The value of g is different for different planets, and on the same planet its value varies from one place to another. In case of planet Earth, for the purpose of computations we approximate the value of g to 9.8 m /s 2. Moon s acceleration due to gravity is 1/6 that of Earth. Video Galileo's Leaning tower of Pisa Pole Video Law of Falling body on the Moon Equator Earth Force Types of Forces Force: It is a push or a pull. Force has both magnitude and direction. Force exist in a variety of situations. Contact Forces: Force is due to physical contact between the bodies. Example mechanical forces. Field Force: No physical contact is necessary to experience the force. Examples are Gravitational, Electrical, Magnetic, and Nuclear Forces. 4
Conversions to remember Force is measured in Newton's (N) Adding Forces -> Net Force What is a Net force? One Kilogram Weighs 9.8 Newton's Relationship between kilograms and pounds 1 kg = 2.2 lb = 9.8 N at Earth s surface 1 lb = 4.45 N Force at other angles can also be added but calculations gets complex for this class Adding Forces Two forces are shown on a spacecraft. What is the net force acting on the ball? (NASA engineers use this concept as gravity assist to veer spacecraft towards other planets without using fuel) a) 3 b) 4 4 c) 5 d) 0 e) -5 3 4 3 Isaac Newton (1643-1727) 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. 5
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. Newton s Second Law of Motion a = F/m F = m a Newton s Laws of Motion (3) Newton s Third Law of Motion 3. To every action, there is an equal and opposite reaction. M = 70 kg V =? What is Newton s Third Law (law of action and reaction)? The same force that is accelerating the boy forward, is accelerating the skateboard backward. m = 1 kg v = 7 m/s Video 1 Video 2 Newton's Laws of Motion 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. 6