HOUSTON COMMUNITY COLLEGE SYSTEMS
SOUTHWEST COLLEGE
COLLEGE PHYSICS I – PHYS 1401
Experiment Two
ADDITION of VECTORS
Professor: David Casntu
Your Name: -----------------
Date: ------------
Lab partners: -----------------
-----------------
-----------------
-----------------
OBJECTIVE
The purpose of this experiment is to study the addition of vectors. This is accomplished by finding the
magnitude and direction of the forces necessary to make a ring centered around a pin located in the
center of a turntable.
THEORY
A vector A can be written as a sum of two vectors Ax and Ay along the x and y axis respectively, as
shown. We call them the components of vector A and are given by:
Ax = A cosθ
Ay = A sinθ
where θ ≤ 900 is the angle between the vector A and the x axis.
In order to find the resultant vector R of a system of vectors A, B, C, etc…
we follow these steps:
a)
Find the x and y components for each vector using the above equations.
i.e find Ax, Bx, Cx ... and Ay, By, Cy ....
Remember they can be positive or negative depending on their direction.
b) Add up these components to get:
Rx = Ax + Bx + Cx + …
Ry = Ay + By + Cy + …
c) now, the magnitude of R is : [Rx2 + Ry2] ½
the direction of R is : ά = tan -1 [Ry / Rx] where ά is
the angle between R and x axis.
If ά > 0 then R is either in the 1st or 3rd quadrant
If ά < 0 then R is either in the 2nd or 4th quadrant.
APPARATUS
Force table
Four weight holders
Four pulleys
Slotted weights
PROCEDURE
1) Suspend a mass of 300 g over a pulley clamped at the 400 angle. Calculate the horizontal and
vertical components and set them up on the force table. Replace now the original force with an
equal force with an opposite direction to it. Check the equilibrium of the system.
2) Suspend a mass of 100 g at 300 and a mass of 200 g at 1200. Find the resultant of these two forces
by the method of components. Check your result by mounting a pulley directly opposite to the
resultant and of same magnitude; the ring should be centered.
3) Keep the same masses above listed and suspend a third mass of 150 g at 2300.
Do the same thing as in procedure 2.
CALCULATION
1) For procedure 2, find, graphically, the magnitude and the direction of the resultant vector.
Use the laws of sine and cosine. Show your graph and work.
2) For procedure 2, find, analytically, the magnitude and the direction of the resultant vector.
Use the method of components.
3) For procedure 3, find, analytically, the magnitude and the direction of the resultant vector.
Use the method of components.
QUESTIONS
1) State in your own words what your conclusion is from this experiment.
2) Could you perform the experiment without the pulleys.Explain their roles.
3) Can the ring be in equilibrium while all the forces acting on it lie in two adjacent plane. Explain.
4) State the condition for translational equilibrium of a particle.