Pre Lab 4

Pre Lab # 4

1. Finding out the Rectangular Components of a Vector is really simple. In order to calculate the X component of a vector you must multiply the Velocity by the Cos of the of the designated angle, and in order to find the Y component of a vector you multiply the Velocity by the Sin of the designated angle.

Example:

Find the rectangular components of the vector 50.0 m/s @ 46 Degrees.

Rx = (50.0 m/s) x (cos 46 Degrees) = 34.7

Ry = (50.0 m/s) x (sin 46 Degrees) = 36.0

2. In order to find the Resultant when adding two or more vectors you must first find the rectangular components for each vector. Once that is done you add the X components together and then add the Y components together to give you the rectangular components of the resultant. In order to get the Velocity of the Resultant you then square each value, add them together, and then find the square root of that value to give you the Velocity of the Resultant. In order to find your resulting angle you simply find the arctan of the value of the Resultant's Y component divided by the Resultant's X component. If your X component for the Resulant is less than zero, you add 180 Degrees to that answer to give you your resulting angle.

Example:

Find the resultant after adding the vectors A = 35.0N @ 143" and B = 25.0N @ 143".

A = 35.0N @ 143"

Ax = 35•cos143 = -27.95

Ay = 35•sin143 = 21.06

B = 25.0N @ 143"

Bx = 25•cos143 = 79.96

By = 25•sin143 = 15.05

Rx = Ax + Bx = -47.91

Ry = Ay + By = 36.11

R = [ (Rx)^2 + (Ry)^2 ]

R = [ (-47.91)^2 + (36.11)^2 ]

R = [ 2,295.37 + 1,303.9 ]

R = [ 3,599.27 ]

R = 59.99 = 60.0N

Tan € = Ry/Rx

ArcTan Ry/Rx = €

ArcTan (36.11) / (-47.91) = -37"

Rx is