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Vector Addition

Vector Addition. You thought you were done with Pythagoras, didn’t you?. Do Now: . What is the difference between mass and weight?. Active Physics Plus 2.3. A quantity that has both magnitude (a size) and direction Velocity! Velocity is speed (which has a size) with a direction (+ or -).

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Vector Addition

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  1. Vector Addition You thought you were done with Pythagoras, didn’t you?

  2. Do Now: • What is the difference between mass and weight?

  3. Active Physics Plus 2.3 • A quantity that has both magnitude (a size) and direction • Velocity! Velocity is speed (which has a size) with a direction (+ or -) • What is a vector? • Example of a vector

  4. Vectors and Scalars • Force – force can be applied in a direction • Acceleration – we can have + or – acceleration • No! Mass only has a size, not a direction so it is scalar (only has magnitude). • Other examples of vectors • Is mass a vector?

  5. Weight • Yes! Weight is a specific force, so it is also a vector. • Is weight a vector?

  6. Addition of forces • Since the force is in the same direction, you simply add the forces together. • 30N+40N = 70N • Two people are pushing on a desk. One applies a force of 30N and another applies a force of 40. What is the total force on the desk.

  7. Addition of forces • Since they are in opposite directions, one of the forces is negative. Let left be the negative direction. • 30N+(-40N) = -10N • Suppose the same two people are now on opposite sides of the desk. One pushes right with a force of 30N and the other pushes left with a force of 40 N. What is the total force on the desk?

  8. What if forces are not in similar directions? • Suppose Kevin kicks the soccer ball towards the goal with a force of 30N and the defender on the other team kicks the ball at the same time with a force of 40 N. What is the total force on the ball?

  9. Addition of forces • Using the Pythagorean theorem. • How do you find the resulting force vector? • What does a vector diagram of this look like?

  10. How to use the Pythagorean Theorem. • What is the Pythagorean Theorem? a = one of the legs of the right triangle b = the other leg of the right triangle c = the hypotenuse of the right triangle

  11. How to Use Pythagorean Theorem • In our example, what are the parts of the triangle? • How do we solve for the resulting force? c b a Given: a = 30N, b = 40N Unknown: c = ? Tool: a2+b2=c2

  12. How to Use Pythagorean Theorem • Solution: • (30N)2+(40N)2=c2 • 900N2+1600N2=c2 • 2500N2=c2 • Take the square root of both sides • 50N = c This means that the soccer ball moved with a force of 50N in an angled direction. • How do we solve for the resulting force?

  13. Practice Problem 1

  14. Practice Problem 1 • Let North be + and South be – • -70N+40N = -30N • This means the resulting force is 30N in the South direction. • What is the resulting force from player A and B?

  15. Practice Problem 1 • What is the resultant force of all three players? • We know in the up down direction, we have a force of 30N in the South Direction. This makes our actual diagram look like 30 N South

  16. Practice Problem 1 • What is the resultant force of all three players? • Given: • 30 N South • 40 N West • Unknown: • Resulting Force • Tool: a2+b2=c2 40 N West 30 N South Resulting Force = ?

  17. Practice Problem 1 • What is the resultant force of all three players? • Solution: • (30N)2+(40N)2=c2 • 900N2+1600N2=c2 • 2500N2=c2 • 50N = c The resulting force is 50 N in the South-west direction 40 N West 30 N South Resulting Force = ?

  18. More Practice Problems Vector Addition Worksheet

  19. Homework: PTG 1-4, 6, 7, 9, 10, 11

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