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Dynamics and Space

Dynamics and Space. Velocity and displacement Vectors and scalars. Learning Outcomes. Vector and scalar quantities: force, speed, velocity, distance, displacement, acceleration, mass, time and energy. Calculation of the resultant of two vector quantities in one dimension or at right angles.

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Dynamics and Space

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  1. Dynamics and Space Velocity and displacement Vectors and scalars

  2. Learning Outcomes • Vector and scalar quantities: force, speed, velocity, distance, displacement, acceleration, mass, time and energy. • Calculation of the resultant of two vector quantities in one dimension or at right angles. • Determination of displacement and/or distance using scale diagram or calculation • Use of appropriate relationships to calculate velocity in one direction.

  3. Lesson 1 • Define what is meant by vector and scalar quantities. • Describe the difference between distance and displacement and speed and velocity. • Calculate the resultant of two vector quantities at right angles to one another.

  4. Scalar And Vector Quantities All physical quantities can be divided into two groups – vectors or scalars. When determining if a quantity is a vector or a scalar you need only ask one question, does direction matter? • A scalar quantity has size (magnitude) only. • A vector quantity has both size and direction.

  5. Distance and Displacement • Distance, d, is how far an object has travelled between two points, regardless of direction. • It is a scalar and is measured in metres. • Displacement, s, is the shortest distance travelled between two points in a straight line. • It is a vector measured in metres and in a particular direction.

  6. Speed and Velocity • Speed and velocity can be calculated by using the following equations: • Speed = distance velocity = displacement time time where speed is a scalar and velocity is a vector. • The direction of the velocity will be the same as that calculated for displacement.

  7. A boy walks 40 m north, then turns back south for 10 m. The journey takes 20 seconds. What is the displacement of the boy the distance the boy travelled the average velocity the average speed s = 40–10 = 30 m north d = 40 + 10 = 50 m v = s / t = 30 / 20 = 1.5 m/s north v = d / t = 50 / 20 = 2.5 m/s Example 1

  8. A car drives 60 km north, then 80 km east, as shown in the diagram. The journey takes 2 hours. Calculate (in km or km/h): the distance travelled the displacement the average speed the average velocity d = 80 + 60 = 140 km s2 = 802 + 602 s = 100 km tan Θ = 80 / 60 Θ =530 W of N / (053) v = d / t = 140 / 2 = 70 km/h v = s / t = 100 / 2 = 50 km/h (053) Example 2 NB: The method used for part b) can also be used to work out resultant forces at right angles.

  9. 2005

  10. 2011

  11. 2008

  12. Lesson 2 • Define what is meant by vector and scalar quantities. • Investigate different quantities to determine if they are vector or scalar. • Identify vector quantities and scalar quantities.

  13. Experiment • You can now carry out experiments to determine if the following quantities are vectors or scalars:

  14. Examples of Vectors and Scalars

  15. 2005

  16. 2008

  17. 2009

  18. 2010

  19. Lesson 3 • Describe how to measure the average speed of an object. • Carry out calculations on the above.

  20. Average Speed • The average speed of a body is found by dividing the total distance travelled by the time of the whole journey. v = d t

  21. Experiment • Measure out a distance and record the time taken to travel that distance. Use the results obtained to calculate your average speed in the table below.

  22. How to measure average speed(3 marks) • Measure out a distance (½) using a ruler (½) . • Record the time taken to travel the distance (½) using a stopwatch (½). • Use the equation: v = d t (1)

  23. 2005 Qu: 21

  24. Thinker Do you know your average speeds?

  25. Lesson 4 • Describe how to measure the instantaneous speed of an object. • Carry out calculations on the above.

  26. Instantaneous Speed • Instantaneous speed is the speed of an object at a particular instance in time. • It is also calculated using v = d / t. • The instantaneous speed is measured over a very small distance and time period.

  27. Experiment

  28. Measuring Instantaneous Speed • Record the length of the mask on the trolley, d, in metres. • Release trolley down slope. • Trolley cuts light gate which then allows the electronic timer to record time, t, in seconds. • Instantaneous speed, v, is calculated using v = d / t.

  29. Experiment Length of mask = m

  30. 2010

  31. 2004 Qu:21

  32. SummaryVelocity and displacement You should now be able to do the following: • Identify vector and scalar quantities from the following: force, speed, velocity, distance, displacement, acceleration, mass, time and energy. • Calculate the resultant of two vector quantities in one dimension or at right angles. • Determine the displacement and/or distance using scale diagram or calculation. • Use of appropriate relationships to calculate velocity in one direction.

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