2: Alternative Vector Addition of Forces Lab
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Use the force table to find the equilibrium force vector of two or more vectors.
2. Use analytical methods for determining the resultant force and equilibrium showing it on the force table.
3. Develop a better understanding of mass, vectors, forces, and weight.
Vectors, terms, and prior knowledge needed:
● Equilibrium - The force vector that can cancel out all of the other forces acting on a point
○ The force that causes this is called an equilibrant
● Resultant vector - The vector that is formed from the result of the combination of two or more vectors
○
○ Vector R is the sum of the individual tension forces that the mass exerts on the string due to the acceleration due to gravity.
○ To get R the x-y components of vectors labeled A, B, and C are added together to get their respective component vectors, which are used to find the magnitude and angle of vector R.
○ With the magnitude and direction of vector R known, an equilibrant can be found by taking the direction angle of vector R and subtracting 180 degrees or by taking the inverse of the component vectors -=<-
,-
>.
● Ideal Pulley - A pulley that has no friction and does not restrict the movement of a string.
● Newton's second law (F=ma) - This lab is based on Newton's second law, Force=mass*acceleration. In this lab, force is the vector that results from the mass of the weights, and acceleration is due to gravity, so a will always be 9.8m/s^2.
Apparatus and tools:
pulley or ideal pulley)
hangers (left) /Mass
(right side top to bottom):
0.5g, 1g, 2g, 5g,10g, 20g, 50g, 100g :
This object has a mass of 5 grams, so
consider that when calculating.
Force table introduction, explanation, and theory:
A force table is a simple setup that can be used to observe vector addition and equilibrium. You can attach one or more pulleys at the edge of the table, and hang a mass on a string that goes through this pulley and to the center connection of all the strings. These hanging masses exert a force downward on the string, and the string pulls back with equal force, called tension. The pulleys remove most of the friction force from the systems that would be introduced if the strings rubbed against the edge of the table. At the center of the table, all of the strings are connected by a ring or clear disk, at the center of that ring, there is a visual representation of whether the forces are in equilibrium. The central string connection is our object of interest, and where we will observe the effect of various forces on this ring. Changing the hanging mass, you can change the magnitude of the force felt by the center string connection. The table surface has labeled angles to set up vectors in specific directions. You can find more information online on how a force table works.
If a mass “m” is hanging over the pulley, the mass has a force downward (the weight
of the mass is m*g, where g is the acceleration from gravity). And the tension on the string is upward. (The magnitude of the tension = m*g)
Set up the force table such that 0 degrees of the table protractor is on your right (just like +x-axis on a Cartesian coordinate system). This means 0° is +x, 90° is +y, 180° is -x, and 270° is -y on your coordinate system.
Resultant vs. Equilibrant
Resultant force is the vector sum of the individual forces acting on the ring. The equilibrant is the force that brings the system to equilibrium.
Force table operation
You will hang some mass on the hangers attached by a thread on the pulley. This means the weight of that mass is a force that has a downward direction, therefore doesn’t have any other directional component that may disrupt the results of the experiment. However, the strings are attached at the center of the force table, and this means the tension force is proportional to the weight (m*g) of the mass used, which is a force acting on the central ring. This means you can set up one or more forces acting on the center connections of all the strings, and calculate their resultant force (resultant, 𝑅). Then you can determine what force (Equilibrant, 𝐸) would balance these forces to bring the system to equilibrium.
Pulley height adjustment
In the first image of this section, the string (highlighted by a red line) is connected to a pulley that is off the table surface, resulting in an inaccurate force measurement. In the second image of this section, the string (highlighted in red) is flat with the surface of the table. In the third image of this section is a green box highlighting the screw to connect to the table like in the first two images. Highlighted by a red circle is a screw that is used to adjust the arms of the pulley and therefore its height. The screw shown in the green box is used to connect the pulley to the force table to conduct the experiment.
Precautions/tips:
- Measure/note the mass of each hanger before you use it.
- The force needed to balance the force table is not the resultant force but the equilibrant force, which is the inverse of the resultant.
- Always calculate and check calculations before experimenting.
- When using mass, take into account that the mass hangers are 5 grams.
- Ex: if you put a mass of 100 grams when doing your math add the mass of the pulley hanger of 5 grams, so the total mass is 105 grams.
- Newtons (N) is measured with si units kilograms, meters, and seconds, not grams.
Experimental I (one force or mass and its Equilibrant):
Step 1: Calculation
do not hang mass yet. You will hang a mass (an example: 100 g) on the blue hanger. The angle should be 0°. Fill out the table below using these values. Remember to take the 5-gram hanger into account for the math.
Finding the resultant vector
Force |
Mass [g] |
Mass [kg] |
Magnitude (mg) [N] |
Angle θ [°] |
X-component [N] |
Y- component [N] |
---|---|---|---|---|---|---|
|
||||||
Resultant force vector = |
*Use kilograms for mass to write force in terms of newtons.
Taking the resultant force and changing it to the equilibrant vector.
Force |
Magnitude |
Angle |
---|---|---|
resultant |
||
Equilibrant |
||
Mass of the equilibrant force: |
Step 2:
Now hang the mass that creates force 𝑨. Then apply the equilibrant force as you
determined in your data table above. To check if the system is actually in equilibrium, remove the central pin (in the force table shown, there is a clear circle at the center with a black circle on the table, which, when in equilibrium, will be aligned with each other). If your system is actually in equilibrium, the ring or clear disk will stay in place otherwise, the masses will be off in the direction of any net force.
Explain your observations
Experiment II (Two forces and their Equilibrant)
*Experiment II will be very similar to Experiment I, but you will have to calculate two masses instead of one.
Step 1: Calculation
Choose two masses to hang and insert into rows , and
then do calculations to find the Resultant force vector.
Force |
Mass [g] |
Mass [kg] |
Magnitude (mg) [N] |
Angle θ [°] |
X-component [N] |
Y- component [N] |
---|---|---|---|---|---|---|
|
||||||
|
||||||
The resultant force vector = |
*Use kilograms for mass to write force in terms of newtons.
Taking the resultant force and changing it to the equilibrant vector.
Force |
Magnitude |
Angle |
---|---|---|
resultant |
||
Equilibrant |
||
Mass of the equilibrant force: |
Experiment III (Three forces and their Equilibrant)
*Experiment II will be very similar to Experiment I, but you will have to calculate two masses instead of one
Step 1: Calculation
Choose two masses to hang and insert them into rows and
then do the calculation to find the Resultant force vector
Force |
Mass [g] |
Mass [kg] |
Magnitude (mg) [N] |
Angle θ [°] |
X-component [N] |
Y- component [N] |
---|---|---|---|---|---|---|
|
||||||
|
||||||
|
||||||
Resultant force vector = |
*Use kilograms for mass to write force in terms of newtons.
Taking the resultant force and changing it to the equilibrant vector.
Force |
Magnitude |
Angle |
---|---|---|
resultant |
||
Equilibrant |
||
Mass of the equilibrant force: |