PASCO ME-9502 Statics System - Manual (Page 22)

S t a t i c s S y s t e m E x p . 3 : R e s o l v i n g F o r c e s — C o m p o n e n t s
®
18 012-12876B
3. What are the magnitudes of F
x
and F
y
, the x- and y-components of F?
• F
x
= _________________ F
y
= ____________________
4. Change the magnitude and direction of the force vector F and repeat the experiment.
5. Record the magnitude and angle of the new force vector, F, and the magnitudes of F
x
and F
y
.
• Magnitude, F = _________________ Angle,
 = ____________________
• F
x
= _________________ F
y
= ____________________
Background
Why use components to specify vectors? One
reason is that using components makes it easier
to add vectors mathematically. The figure shows
the x- and y-components of a vector of length F,
and an angle
 with respect to the x-axis. Since
the components are at right angles to each other,
the parallelogram used to determine their result-
ant is a rectangle. Using right triangle AOX, the
components of F can be calculated:
• F
x
, the x-component of F is F cos

• F
y
, the y-component of F is F sin

If you want to add several vectors, find the x- and
y-components for each vector. Add all the
x-components together and all the y-components
together. The resulting values are the x- and
y-components for the resultant. The magnitude of the resultant, F
R
, is the square root of the sum of the squares of
the resultant’s x-component (R
x
) and the y-component (R
y
).
The angle of the resultant is the arctangent of the y-component divided by the x-component.
Procedure 2
Make sure that the Force Wheel is level. Set up a new force, F. Put one thread from the force disk over a pulley and
tie a mass hanger to the end of the thread. Add mass to the mass hanger.
1. Calculate and record the magnitude of the force, F, that you set up with the pulley and mass hanger. Use the
Force Wheel to determine the angle.
• Magnitude, F = _________________ Angle,
 = ____________________
2. Calculate the magnitudes of F
x
and F
y
, the x- and y-components of the new force, F. (Remember, F
x
= F cos

and F
y
= F sin
.)
• F
x
= _________________ F
y
= ____________________
3. Now, set up the Spring Scale with a pulley and a thread from the force disk so it can apply the x-component,
F
x
, of the new force F. Adjust the Spring Scale so that it pulls the force disk horizontally by the amount, F
x
.
4. Next, attach a mass hanger to the third thread from the force disk so the thread hangs vertically. Add mass to
the hanger so it pulls the force disk vertically by the amount, F
y
.
F
F
x
= F cos

F
y
= F sin

O X

Figure 3.2: Vector components
F
R
R
x
  2
R
y
  2
+ =

R
R
y
R
x
------  
 
atan =