Vector Addition You thought you were done with

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 � Force � Is � No! mass a vector? – force can be applied in a direction � Acceleration – we can have + or – acceleration 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 30 N 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. ◦ 30 N+40 N = 70 N

Addition of forces � Suppose the same two people are now on opposite sides of the desk. One pushes right with a force of 30 N 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. ◦ 30 N+(-40 N) = -10 N

What if forces are not in similar directions? � Suppose Kevin kicks the soccer ball towards the goal with a force of 30 N 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? c b a � How do we solve for Given: a = 30 N, b = 40 N the resulting force? Unknown: c = ? Tool: a 2+b 2=c 2

How to Use Pythagorean Theorem � How do we solve for� Solution: the resulting force? ◦ (30 N)2+(40 N)2=c 2 ◦ 900 N 2+1600 N 2=c 2 ◦ 2500 N 2=c 2 ◦ Take the square root of both sides ◦ 50 N = c This means that the soccer ball moved with a force of 50 N 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 – ◦ -70 N+40 N = -30 N ◦ This means the resulting force is 30 N 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 30 N 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? 30 N 40 N West Resulting Force = ? South � Given: ◦ 30 N South ◦ 40 N West � Unknown: ◦ Resulting Force � Tool: a 2+b 2=c 2

Practice Problem 1 � What is the resultant force of all three players? 30 N South 40 N West � Solution: Resulting Force = ? ◦ (30 N)2+(40 N)2=c 2 ◦ 900 N 2+1600 N 2=c 2 ◦ 2500 N 2=c 2 ◦ 50 N = 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