Physics

1. Physics Notes Chapter 2 Motion in One Dimension

2. 2.1 Position • Position: The location of an object; in physics, typically specified with graph coordinates. • Can be measured on a number line • Points on the line specify a given position

3. 2.2 Displacement • Displacement – The direction and distance of the shortest path between an initial and final position. • Has both magnitude and direction • Vector quantity • Δx gives a change in position or displacement • Measured in meters • Motion – A displacement of an object in relation to objects that are considered to be stationary

4. Speed • Speed – The time rate of motion • If the slope of a displacement vs. time graph is constant (straight line) the speed is constant. • Average speed is total distance divided by elapsed time Speed = distance/time (m/s). • Instantaneous Speed – for objects with varying speed the slope of a line tangent to the curve on a displacement vs. time graph gives instantaneous speed • Both instantaneous and average speed are scalar.

5. 2.3 Velocity • Velocity – is speed in a particular direction. • Both magnitude and direction are specified. • Velocity is a vector quantity • Units are m/s

6. 2.4 Average Velocity • Average velocity (ν) is total displacement divided by elapsed time. • Average velocity equals displacement divided by the time it takes for the displacement to occur. • This is not the numeric average of several velocities.

7. 2.5 Instantaneous Velocity • Instantaneous velocity- speed and direction at a given moment in time. • Given by the slope of a line tangent to the position vs. time graph at that point. • Physicists usually mean “instantaneous velocity” when they say “velocity” because instantaneous velocity is often more useful than average velocity. Typically, this is expressed in statements like “the velocity when the elapsed time equals three seconds.”

8. 2.6 Position-time graph and velocity • A graph of an object's position over time is a useful tool for analyzing motion. • The slope of a straight line between any two points of the graph is the object’s average velocity between them. • The slope of the tangent line for any point on a straight-line segment of a position-time graph is constant. When the slope is constant, the velocity is constant.

9. Time Position 0 0 10 10 20 20 30 30 40 30 50 20 60 10 70 0 Velocity Graph

10. 2.7 Drawing Position Time Graphs kbooksprinc://principles_of_physics/02_Motion%20in%20One%20Dimension/06/sp.html Section 2.8 Interactive problem: match a graph using velocity http://127.0.0.1:26300/Principles_of_Physics/02_Motion%20in%20One%20Dimension/08/sp.html Section 2.9 Velocity graph and displacement http://127.0.0.1:26300/Principles_of_Physics/02_Motion%20in%20One%20Dimension/09/sp.html

11. Solving Velocity Vector Problems • Graphic – Draw a picture using tip to tail construction – the diagonal of the parallelogram is the resultant. • Trigonometry- use SOHCAHTOA and law of sines or cosines if needed. OR Use vector resolution as discussed in Chapter 1

12. 2.10 The Nature of Acceleration • Acceleration is the time rate of change of velocity in m/s/s or m/s2. • Constant acceleration produces a straight line on a velocity vs. time graph. The slope of the line is acceleration. • Variable acceleration produces a curve on a velocity vs. time graph. The instantaneous acceleration is the slope of the line tangent to the curve at the given point.

13. Solving Acceleration Problems • Galileo – Acceleration down a plane and acceleration of a falling body follow the same mathematical rules. • The final velocity of a an object starting from rest and accelerating at a constant rate equals the product of the acceleration and elapsed time. • If the object has initial velocity then final velocity will equal the sum of the initial velocity and the increase in velocity produced by the acceleration.

14. Acceleration Equations and and so and Expanding terms and solving for Vf

15. Acceleration Equations Cont… With initial velocity Starting from rest

16. Acceleration & Velocity-Time Graphs Time Velocity 0 10 1 15 2 20 3 20 4 10 5 0 6 -10

17. Freely Falling Bodies • Value of acceleration due to gravity varies on Earth’s surface but is generally close to 9.80 m/s2 • Equations for acceleration and free fall are the same but substitute g for a. g = 9.80 m/s2 • Vectors d & v are assigned + for down – for up

18. Newton’s Law of Universal Gravitation • The force of attraction between two objects is directly proportional to their masses and inversely proportional to the square of the distance between their centers of mass • G= 6.67x10-11 N.m2/kg2

19. The Mass of the Earth SO BUT Fw = mpg Therefore SO and • G= 6.67x10-11 N.m2/kg2 and g=9.80 m/s2 and d= 6.37x106 m • Solving for me we get me= 5.96x1024 kg as the mass of Earth

20. Relation between Gravity and weight • Gravity – Used to describe the force of gravitation on an object on or near the surface of a celestial body, such as Earth. • This force is inversely proportional to the square of the distance from the center of the body to the center of the Earth (2x the distance=4x less force) • Since weight is proportional to gravity weight varies with distance from the center of the Earth.

21. Gravitational Fields • Value of g at a particular point is the gravitational field strength at that point. • A gravitational field is a region of space in which each point is associated with a vector with the value of g, or the force of gravitation exerted on a 1 kg mass at that point. • In the field concept objects are surrounded by regions that exert forces on masses in those regions. • The nature and origin of gravitational force is still unknown.