**Figure 6-1: Graphical Representation of Forces**

On the force table, equilibrium is indicated by the ring to which the
strings are attached. At equilibrium, this ring is centered on the pin
at the center of the table. After getting apparent equilibrium, remove
the pin and gently move the ring a short distance from the center position
and observe whether the ring returns to the exact position as it should.
This procedure will help to make certain that the forces are due to the
weights (masses) and not due to friction in the pulleys. **Do not tie
any additional loops or knots in the strings**.

Ý

**2.** Place a second pulley at** * **degrees,
and suspend a total weight of 1.47 N (150 g) over this pulley. This will
be called force

***** **YOUR INSTRUCTOR WILL PROVIDE YOU WITH
THE ANGLES TO BE USED HERE**

**3.** By trial and error, determine the position of the third pulley
and the force in newtons necessary to exactly balance the other two forces.
This third force is the **EQUILIBRANT**. It is opposite in direction
and equal in magnitude to the **RESULTANT **of the first two forces.

**4.** Open up the Force Table Workbook link
and fill out the header information, and enter
the forces used and their angles in the **PROCEDURE 1** area in the
**DATA** Table.

**5. **Open up the Force Table Graphics Sheet link.
Use the **STRAIGHT LINE **graphics
tool to draw a vector to represent **FORCE A**. Since it is about **3N**,
a convenient scale is to **let 1N = 2cm** on the drawing. The appropriate
vector arrow can be drawn by doing the following:

***** **Select the STRAIGHT LINE tool.**

*** Holding the SHIFT KEY down, hold the mouse button down at a starting
point and continue to the end 6cm away.**

**You should get a HORIZONTAL arrow that is 6cm
(3N) long.**

*** Make sure that LAYOUT....SHOW SIZE
is selected. Click the mouse on Force A and you should see a display of
numbers at the bottom of the window. These readouts are: horizontal component,
vertical component, angle measured from the +x-axis, and total magnitude.**

*** With the vector still selected (sizing boxes at each end) choose
ARRANGE...ROTATE from the menu.**

*** Drag the TIP of the Force A until the angle reading is equal to
what you had in the measurement set up (cell C10).**

*** Slide the vector down so that its tail is located at the RED
RESOLUTION ORIGIN.**

**BE CAREFUL NOT TO GRAB IT WITH THE SIZING
BOXES!**

**You may need to practice a few times to master the procedure.**

**6. **Do exactly the same thing with **FORCE B**, which is nearly
**1.5N** or **3cm** long on the scale.

**7.** At this point, you should have 2 forces with their tails on
the **RED** origin. Select **FORCE B**
with the mouse. Select the menu **EDIT....DUPLICATE**.
This operation produces a duplicate of the Force B vector directly on top
of it. Grab it with the mouse (being careful **NOT** to grab on the
sizing boxes) and slide it until its **TAIL** coincides with the **TIP**
of the **FORCE A** vector. This is the process of vector addition and
you can now find the **RESULTANT** (sum) of the two forces.

**8. **Draw the **RESULTANT** with the **STRAIGHT
LINE** tool. Do **NOT** use the **SHIFT
KEYÝ** in this process! It is a vector that begins at the **ORIGIN**
and ends at the **TIP** of the transferred
**FORCE B** vector.

**9.** Click and Hold on the **RESULTANT. **Observe and record
the magnitude and angle of this force on the __Force Table Workbook__
where indicated in **ANALYSIS A**.

**10. **Compare the magnitude of the **RESULTANT** with the value
measured for the **EQUILIBRANT**. __Make sure__ you convert from
the drawing scale back to Newtons! Find the **PERCENTAGE DIFFERENCE**
between the two values.

**11.** Return to the __Force Table Graphics Sheet__ and **CLICK**
**and** **HOLD** on **FORCE A**. Record its x- and y-components
on the __Force Table Workbook__ in **ANALYSIS B**. BE CAREFUL about
the algebraic signs of the components-the Graphics Sheet always gives a
positive value. __Repeat__ for **FORCE B**.

**12.** Add up the components separately to obtain the x-component
and the y-component of the **RESULTANT**. **HINT:**
you can let the spreadsheet do the work by entering in cell E18 the following:
"= C18 + D18"; and in cell E19: "= C19 + D19".

**13. **From the two components, calculate the **MAGNITUDE** of
the **RESULTANT** and enter its value in the __Force Table Workbook__.
**HINT:** In cell E21 enter: "SQRT(E18^2
+ E19^2)". This formula simply squares the components, adds them and takes
the square root.

**14. **Compare the **MAGNITUDE** that you have computed with
the **MAGNITUDE** of the **EQUILIBRANT**. Find the **PERCENTAGE
ERROR** and enter it into the spreadsheet.

**15. **Return to the __Force Table Graphics Sheet__ , and choose
under **EDIT.....SELECT ALL**. Select **EDIT....COPY**
and **EDIT....PASTE** at cell A24
on the Worksheet. Resize as necessary.

**PROCEDURE 2**

**1.** Repeat the procedure and calculations of **PROCEDURE**
**1** except to place the first pulley at ** *
**and the second pulley at

**2.** Return to the __Force Table Graphics Sheet__ , and choose
under **EDIT.....SELECT ALL**. Select **EDIT....COPY**
and **EDIT....PASTE** at cell A56
on the Worksheet. Resize as necessary.

**PROCEDURE 3**

**1.** In this procedure, you are to determine the equilibrant of
__three__ forces by experiment. Place the first pulley at 0.0^{o}
and suspend a total weight from it of 0.685 N (70 g). Place a second pulley
at ** * **adegrees, and suspend a
total weight of 1.47 N (150 g) over it. Place a third pulley at

**2. **Repeat the same procedures as above, except now you will have
three forces to find the resultant for. As before find the **MAGNITUDE**
of the **RESULTANT** by using the **SIZE** data on the __Force Table
Graphics Sheet__ . Compare with the measured **MAGNITUDE** of the
**EQUILIBRANT** and compute the **PERCENTAGE DIFFERENCE**. All of
these results are to be recorded in the __Force Table Workbook__ as
indicated there.

**3.** Using the drawing in the __Force Table Graphics Sheet,__
determine the values of the components of all three forces and record them
in the __Force Table Workbook__. Perform the calculation to find the
components of the RESULTANT and from these values, the MAGNITUDE of the
RESULTANT. Use the spreadsheet functions whenever feasible. Compare with
the MAGNITUDE of the EQUILIBRANT, and compute the PERCENTAGE ERROR.

**4. **Return to the __Force Table Graphics Sheet__ , and choose
under **EDIT.....SELECT ALL**. Select **EDIT....COPY**
and **EDIT....PASTE** at cell A89 on the
__Force Table Workbook__. Resize as necessary.

**5. PRINT** the __Force Table Workbook__ and turn it in to your
instructor.