You thought you were done with Pythagoras, didn’t you? 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 What is a vector? Example of a vector A quantity that has both magnitude (a size) and direction Velocity! Velocity is speed (which has a size) with a direction (+ or -)

Vectors and Scalars Other examples of vectors Is mass a vector? 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).

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

Addition of forces 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. Since the force is in the same direction, you simply add the forces together. 30N+40N = 70N

Addition of forces 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? Since they are in opposite directions, one of the forces is negative. Let left be the negative direction. 30N+(-40N) = -10N

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?

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

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

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

How to Use Pythagorean Theorem How do we solve for the resulting force? 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.

Practice Problem 1

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

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

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

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

More Practice Problems Vector Addition Worksheet

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