Relative motion & vector addition

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Relative motion & vector addition

  1. 1. Stage 6 Physics – Moving About Why do head on crashes cause so much damage?
  2. 2. What is moving? <ul><li>Is the car moving? </li></ul><ul><li>Is the road moving? </li></ul><ul><li>Is the snow moving? </li></ul><ul><li>Are you moving? </li></ul>
  3. 3. What is moving? <ul><li>If you are in an elevator without signs or lights, how do you know if you are going up or down or that you are moving at all? </li></ul>
  4. 4. It’s all relative <ul><li>Velocity is measured according to a frame of reference . </li></ul><ul><li>We usually talk about velocity being relative to a stationary Earth. </li></ul><ul><li>But the Earth is moving at 30 km s -1 around the sun, and the sun is orbiting around the centre of the galaxy. </li></ul><ul><li>There is no absolute rest frame of reference. </li></ul>
  5. 5. Relative velocity <ul><li>Relative velocity is the velocity of an object measured by a moving observer. </li></ul><ul><li>The relative velocity is the difference between the velocity of the object relative to the ground and the velocity of the observer relative to the ground . </li></ul>
  6. 6. Relative velocity - example <ul><li>You are in a car travelling at a constant velocity of 90 km h -1 west on a straight road. The car ahead of you is travelling at a constant speed of 100 km h -1 in the same direction. </li></ul>100 km h -1 90 km h -1
  7. 7. Relative velocity - example <ul><li>What is the car’s velocity relative to the ground? </li></ul><ul><li>100 km h -1 </li></ul><ul><li>What is the car’s velocity relative to you? </li></ul><ul><li>Remember: relative velocity is the difference between the velocity relative to the ground and the velocity of the observer relative to the ground. </li></ul><ul><li>We will make west + and east -. </li></ul><ul><li>100 km h -1 – 90 km h -1 = 10 km h -1 . </li></ul><ul><li>Since the answer is positive, and we made + west, the relative velocity of the car to you is 10 km h -1 west. </li></ul>
  8. 8. Relative velocity – another example <ul><li>You are driving at 90 km h -1 west. Another car is travelling towards you at 100 km h -1 east. </li></ul>
  9. 9. Relative velocity – another example <ul><li>What is the car’s velocity relative to you? </li></ul><ul><li>Let’s say west is + and east is -. So your velocity is +90km h -1 and the car’s velocity is -100 km h -1 . </li></ul><ul><li>Relative velocity = object’s velocity relative to the ground – observer’s velocity relative to the ground. </li></ul><ul><li>Relative velocity = -100 km h -1 – 90 km h -1 </li></ul><ul><li>= -190 km h -1 </li></ul><ul><li>= 190 km h -1 east </li></ul>
  10. 10. Head on collisions <ul><li>This is why head on collisions cause so much damage – the relative velocities add together! </li></ul><ul><li>If you’re travelling at 60 km h -1 and you hit a car travelling towards you at 60 km h -1 , the car’s relative velocity towards you will be 120 km h -1 . </li></ul>
  11. 11. Vector addition <ul><li>Remember: vectors are quantities with a magnitude and a direction. </li></ul><ul><li>We can represent vectors such as displacement, velocity and acceleration with vector diagrams (they are just arrows) </li></ul>
  12. 12. Vector addition <ul><li>Arrows need to be to scale. </li></ul><ul><li>Every vector arrow has a tail end and a tail head. </li></ul><ul><li>Basically, instead of describing object’s displacement/velocity/acceleration/force in words, we use vector diagrams to indicate magnitude and direction. </li></ul>This vector has half the magnitude of the other vector This vector has twice the magnitude of the other vector Tail end Tail head
  13. 13. Vector addition <ul><li>We use vector diagrams to visually represent word problems. </li></ul><ul><li>It is easier to draw arrows to show magnitude and direction and to write a whole paragraph. </li></ul>

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