All About Motion  Displacement, Velocity and Acceleration


 Cornelius Johnson
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1 All About Motion  Displacement, Velocity and Acceleration Program Synopsis minutes Teacher Notes: Ian Walter Dip App Chem; GDipEd Admin; TTTC This program explores vector and scalar quantities and their units, and methods of representing vectors and arithmetic operations with vectors. Distance and displacement are defined, and numerical examples are used. Speed and velocity are investigated and specific numerical examples of their uses are given, including the special case of uniform circular motion. Acceleration is defined in terms of velocity change with time, including negative acceleration and an analysis of centripetal acceleration of a body moving in a circular path with constant speed. Galileo s inclined plane experiment is discussed and numerical observations are used to calculate acceleration on inclined planes. To order or inquire please contact VEA: VEA Inc Website: 10 Mitchell Place Suite 103 White Plains, NY Toll Free: Facsimile:
2 Related Programs Energy Rules The Conservation of Energy and Momentum Methods of Heat Transfer The Advance Physics Series 1. The Synchrotron (The Advance Physics Series) 2. Photonics (The Advance Physics Series) 3. Special Relativity (The Advance Physics Series) 4. Light, Phase and Matter (The Advance Physics Series) 5. Sound and Other Demonstrations (The Advance Physics Series) Introduction This program introduces senior students to the concepts of scalar and vector quantities. Excellent graphics and examples of calculations with arithmetic operations with vectors are provided for students to gain a sound understanding of the terms used in kinematics. Students will be clearly shown the differences between scalar and vector quantities by using familiar everyday examples. Uniform circular motion and motion on an incline are addressed in detail. Program Rationale This program will help senior students reinforce the theory taught in the classroom on kinematics. The graphics in the program are essential for visual learners in their understanding of the concept of vectors and scalars and the mathematical operations used with these quantities. This program aims to provide teachers and students with an uptodate overview of the basics of theory and practice in kinematics. Program Timeline 00:00:00 Introduction: All About Motion 00:01:28 Vectors 00:04:27 Displacement 00:08:22 Velocity 00:11:55 Acceleration 00:15:41 Acceleration on Galileo's inclined planes 00:19:19 Credits 00:20:03 End of program Useful Resources Books and Other Print Resources Daish, CB (1972) Physics of Ball Games. The English Universities. Griffing, DF (1987) The Dynamics of Sport, datalog Schrier, EW and Allman, WF (eds) (1987) Newton at the Bat. The Science in Sports. Macmillan: New York
3 Worksheet Before the DVD 1. Using the internet, or other suitable reference, provide a 100 word report on Scalar and vector quantities. In your report, list and describe as either scalar or vector, six common quantities used in physics. 2. Discuss with the person next to you how an object travelling in a circular path with constant speed is accelerating. 3. In small groups, discuss addition and subtraction of vectors that have the same direction with the same, or opposite sense. Discuss the necessary mathematical operations required when adding and subtracting similar vector quantities that are perpendicular to each other
4 During the DVD 1. What is the one property possessed by all physical quantities? 2. What name is given to physical quantities with magnitude only? 3. What name is given to physical quantities that have both magnitude and direction? 4. How can a vector quantity be represented on a diagram? 5. Vector quantities of the same type can be added. What method is used to subtract vectors of the same type? 6. What is the difference between distance and displacement? 7. What is the difference between speed and velocity? 8. Write a formula to calculate average speed. 9. Write a formula to calculate average velocity. 10. Explain why an object travelling in a circular path with constant speed has a changing velocity. 11. Write a formula to calculate average acceleration
5 12. Vectors of the same type that do not have the same direction or sense can be added and subtracted. Describe a method that can be used for these operations on vectors. 13. Why did Galileo use an inclined plane to investigate the law of falling instead of just dropping an object? 14. In what way does an inclined plane dilute gravity? 15. Why did Galileo use an angle of 8 O for the incline? 16. What factors may influence the rate at which a ball will roll down an incline? 17. Write a formula relating acceleration down an incline, the angle of the incline, and acceleration due to gravity. 18. Why must all physical quantities be precisely defined?  5 
6 After the DVD Worksheet 1. Complete the following table by placing each of the listed physical quantities in the correct column: distance displacement speed velocity time force mass acceleration scalar vector 2. Represent a force of 10 N west on a vector diagram using a scale of 2.0 N 1.0 cm. 3. Perform the following vector additions; 2.0 m north m south 10 N east N east 1.0 N south N east 4. Perform the following vector subtractions; 10 m west m west 20 N south  10 N north 1.0 N west N south 5. A car travels from town A, a distance of 100 km along the road to town B in a time of 2.0 hours. Town B is 80 km north east of town A. a) Calculate the average speed of the car between town A and town B. b) Calculate the average velocity of the car between town A and town B. 6. Use the information in the table below to calculate the acceleration of a ball rolling uniformly from rest down a smooth incline. Distance travelled during time (m) time (s) In the absence of frictional forces and given the acceleration due to gravity is 9.8 m s 2, calculate the angle in degrees of the incline
7 Suggested Student Responses During the Program 1. What is the one property possessed by all physical quantities? The one property possessed by all quantities is magnitude. 2. What name is given to physical quantities with magnitude only? Quantities with magnitude only are called scalar quantities. 3. What name is given to physical quantities that have both magnitude and direction? Vector quantities have both magnitude and direction. 4. How can a vector quantity be represented on a diagram? A vector quantity may be represented on a diagram by drawing the magnitude of the vector to a given scale and indicating the direction with an angle from a reference point, or by positive or negative signs. 5. Vector quantities of the same type can be added. What method is used to subtract vectors of the same type? When vectors of the same type are subtracted from one another, the sense of the vector being subtracted is reversed and the two vectors are added. 6. What is the difference between distance and displacement? Distance is a scalar quantity and requires magnitude only. Displacement is a vector quantity that requires both magnitude and direction. 7. What is the difference between speed and velocity? Speed is a scalar quantity and requires magnitude only. Velocity is a vector quantity that requires both magnitude and direction. 8. Write a formula to calculate average speed. Average speed = distance Time 9. Write a formula to calculate average velocity. Average velocity = displacement (or change in position) time for the change 10. Explain why an object travelling in a circular path with constant speed has a changing velocity. The object is continually changing direction as it moves in a circular path. Since the direction is constantly changing, although the magnitude (speed) is constant, the object has a changing velocity
8 11 Write a formula to calculate average acceleration. Average acceleration = change in velocity time for the change 12 Vectors of the same type that do not have the same direction or sense can be added and subtracted. Describe a method that can be used for these operations on vectors. Vectors of the same type but with different directions can be added and subtracted using vector diagrams of the vectors drawn to scale with their respective directions. The resultant vector may be measured and then compared with the scale to determine its magnitude, and its direction may be found using a protractor to measure angles from a reference point. 13 Why did Galileo use an inclined plane to investigate the law of falling instead of just dropping an object? Galileo used an incline to dilute the action of gravity. Timing devices used at this time were unable to measure short time intervals. 14 In what way does an inclined plane dilute gravity? An object will roll down an inclined plane due to the action of gravity forces. The angle of the incline is related to the acceleration due to gravity. By altering the angle of the incline, accelerations of objects down the plane can be varied between zero and 9.8 m s Why did Galileo use an angle of 8 O for the incline? Galileo used an angle of 8 O so that timing with a water clock would give sufficiently accurate values for a reasonable distance measurement down the incline. 16 What factors may influence the rate at which a ball will roll down an incline? Some factors that would influence the rate at which a ball will roll down an incline are: the angle of the incline, the roughness of the surface of the incline, the size of the ball, (larger more air friction) the material of which the ball is made (light material more air friction). 17 Write a formula relating acceleration down an incline, the angle of the incline, and acceleration due to gravity. a = acceleration down the incline, g = acceleration due to gravity, θ = angle of the incline. a = g sin θ 18 Why must all physical quantities be precisely defined. All physical quantities must be precisely defined so that there will be no confusion regarding these quantities when used in scientific papers and calculations. The definitions of these quantities are determined by international panels and are accepted world wide. The metre, the basic unit of length, can be defined in terms related to the wavelength of a particular electromagnetic radiation
9 After the DVD Suggested student responses Worksheet 1. Complete the following table by placing each of the listed physical quantities in the correct column Distance displacement speed velocity time force mass acceleration scalar distance speed time mass vector displacement velocity force acceleration 2. Represent a force of 10 N west on a vector diagram using a scale of 2.0 N 1.0 cm. 10 N west (arrow points west) 5.0 cm 3. Perform the following vector additions; 2.0 m north m south 10 N east N east 1.0 N south N east = 0 = 15 N east = 1.4 N south east + = 1.0 N south 1.0 N east 4. Perform the following vector subtractions; 10 m west m west 20 N south  10 N north 1.0 N west N south = 2.0 m west = 20 N south + 10 N south = 30 N south = 1.0 N west N north = 1.0 N west + = 1.4 N north west 1.0 N north  9 
10 5. A car travels from town A, a distance of 100 km along the road to town B in a time of 2.0 hours. Town B is 80 km north east of town A. (a) Calculate the average speed of the car between town A and town B. Average speed = distance travelled Time = 100 km 2.0 hr = 50 km h 1 (b) Calculate the average velocity of the car between town A and town B. average velocity = displacement time = 80 km north east 2.0 hr = 40 km hr 1 north east 6. Use the information in the table below to calculate the acceleration of a ball rolling uniformly from rest down a smooth incline. distance travelled during time (m) time (s) The distance travelled during each second after the first increases constantly by 2.0 m. So the average speed constantly changes at 2.0 m s 1 each second. The acceleration (down the incline) = 2.0 m s In the absence of frictional forces and given the acceleration due to gravity is 9.8 m s 2, calculate the angle in degrees of the incline to the nearest whole number. a = g sin θ a sin θ = g 2.0 = 9.8 θ = 12 o
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