Forces in Two Dimensions
Trig Review:
Sin, Cos, and Tan only work in a RIGHT TRIANGLE.
SOHCAHTOA ,an ancient Hawaiian word.
opp
Sin( x) 
hyp
adj
Cos( x) 
hyp
opp
Tan( x) 
adj
Math Review:
Pythagorean Theorem:
A B C
2
Pythagorean Theorem only works in RIGHT TRIANGLES
2
2
Math Review:
Law of Cosines:
A  B  2 AB cosc  C
2
Law of Cosines works in ANY TRIANGLE
2
2
Math Review:
Law of Sines:
Law of Sines works in ANY TRIANGLE
sin a  sin b  sin c 


A
B
C
Components
of
Vectors
Sometimes it is helpful to add vectors by breaking them into their X and Y
Components.
1. Use Sin to find the y component.
2. Use Cos to find the x component.
3. Then add up all the x component directions and y component directions.
4. Use the Pythagorean theorem to find the magnitude of the resultant.
5. Use the inverse Tangent to find the angle of the resultant.
Find the resultant of the following system of forces.
A crate weighing 562 N is resting on a plane inclined at 30.0 degrees above the
horizontal. Find the components of the weight forces that are parallel and
perpendicular to the plane.
A force of 50.0 N accelerates a 55 kg sheep at 0.33 m/s2
across a floor.
A) What is the frictional force.
B) What is the coefficient of friction?
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Forces in Two Dimensions