Physics 10/19

Physics 10/19

Vectors in Two-Dimension

Open Ended

Two students are helping me move a table. They are both pushing it to the right with 40 N of force, what is the net force on the table?

Test Explanations

Vectors revisted

• In your journal question you had two students pushing together with a force of 40 N to the right.

• The sum of the forces is 80 N to the right, which you should probably expect.

• But how do you find the sum of those force vectors?

• Remember, when adding vectors along a straight line, the resultant vector always points from the tail of the first vector to the tip of the final vector.

• Does this rule still apply when the vectors do not lie in a straight line?

Adding vectors in two dimension

• Even when vectors do not lie on a straight line, the resultant vector always points from the tail of the first vector to the tip of the final vector.

• You can you a protractor and a ruler to draw the vectors at the correct angles and also measure the magnitude and direction of the resultant vector.

• Let's go to the board...

Perpendicular vectors

• You can also use trigonometry to determine the length and direction of the resultant vectors.

• Remember, you can use the Pythagorean Theorem to find the lengths of a right triangles sides.

• We use the Pythagorean Theorem as follows:

• R² = A² + B²

Angles other than 90 degrees

• If you are adding two angels that are an angle other than 90 degrees, then you can use the law of sines or the law of cosines

Law of Sines

• Best used when you are given two angle measurements and one only one vector magnitude

• R/sin $\theta$  = A/sin a =B/sin b

Law of Cosines

• Useful when given the angle between two vectors with know magnitudes.

• R2 = A2 + B2 - 2AB cos $\theta$  

If  $\theta$  = 90 degrees

Then the triangle is a right triangle and the law of cosines reduces to the pythagorean theorem.

Practice Promblems

Open Ended

Exit Ticket - Why does the law of cosines work on both perpendicular vectors as well as vectors other than 90 degrees?