Vector Additon of Forces
Purpose: The purpose of this lab was to study vetor additon by graphical means and by using components. A circular force table was given to check results.
Procedures: Our instructor assigned 3 magnitudes and 3 angles to us and asked that we added them together and come up with the magnitude and direction of the resultant force using a ruler and protractor.
The Vectors were as following, 200 @ 0 degrese,
100 @ 41 degrese, & 150 @ 132 degrese. With our ruler and protractor we sketched the vectors and found our resultant vetor. Our resultant force was 250 @ 45 degrese.
After our findings we constructed a second vector diagram showing
the same three forces but this time we used components to find our
resultant vector. This was done by first finding & then combining
like igen values. Egin values are what make up components. The
i hat component is assigned to the x axis and the j hat component is
assigned to the y axis. Together they form a vector.
To find our
values we had to use some trig.
We use the formula magnitude
times cos inverse of the angle to
find the x component & magnitude
times sin inverse of the angle to find the
y component.
When we were finished with ur diagram we then drew the exact force vector that would be needed to cancel out the resultant. At first I had no idea of why we had to find and draw this vector that would cancel the resultant. But it would all come together as the lab progressed.
Materials : For this lab we used a circular force table,
masses, mass holders, string, protractor, &
four pulleys.
We mounted three pulleys
to the force table at the angles given to us. Strings were attached to the center ring and conected to the mass holder. Each mass was hanged with its appropriate forces in grams on each string. The ring hang to a side and this meant that it was not in Equilibrium. We then set up the fourth pulley and mass holder at 180 degrees opposite from the angle we had calculated for the resultant vector of the first three vectors. With a mass equal to the magnitude of the resultant placed on the fourth holder we got our table to balance.
This last step was the prove of equilibrium.
Now we had to confirm our results via simulation: @
Http://phet.colorado.edu/en/simulation/vector-addition
In this system we toke some vectors and added them together. This was done by grabbing some errows form a bucket and giving them component values. Once our first vector was drawn we continued doing this with other vectors but this time adding them together by conecting the head of one vector to the tail of the other. When this was done we checked a box that said add vectors and the system added them up for us giving us the resultant vector with its values. It was the same one we had gotten
Source of error: When drawing vectors with ruler and protractor we found that there was a slight diffrence on our resultant vectors magnatude and direction. This method wasnt as accurate as when we added by components.
Conclusion: In this lab I learned that when you want to get the force vector that would be needed to set equilibrium you must get the displacement and subtract it from the tail of the resultant vector. Or in simpler words to get equilibrium you must have a vector that is both equal in magnitude but opposite in direction, more specific 180 degrees opposite from the angle of our resultant vector. Once again our resultant vector is the resultant displacement of the added vector components.
values we had to use some trig.
We use the formula magnitude
times cos inverse of the angle to
find the x component & magnitude
times sin inverse of the angle to find the
y component.
masses, mass holders, string, protractor, &
four pulleys.
We mounted three pulleys
to the force table at the angles given to us. Strings were attached to the center ring and conected to the mass holder. Each mass was hanged with its appropriate forces in grams on each string. The ring hang to a side and this meant that it was not in Equilibrium. We then set up the fourth pulley and mass holder at 180 degrees opposite from the angle we had calculated for the resultant vector of the first three vectors. With a mass equal to the magnitude of the resultant placed on the fourth holder we got our table to balance.
This last step was the prove of equilibrium.
Now we had to confirm our results via simulation: @
Http://phet.colorado.edu/en/simulation/vector-addition
In this system we toke some vectors and added them together. This was done by grabbing some errows form a bucket and giving them component values. Once our first vector was drawn we continued doing this with other vectors but this time adding them together by conecting the head of one vector to the tail of the other. When this was done we checked a box that said add vectors and the system added them up for us giving us the resultant vector with its values. It was the same one we had gotten
Conclusion: In this lab I learned that when you want to get the force vector that would be needed to set equilibrium you must get the displacement and subtract it from the tail of the resultant vector. Or in simpler words to get equilibrium you must have a vector that is both equal in magnitude but opposite in direction, more specific 180 degrees opposite from the angle of our resultant vector. Once again our resultant vector is the resultant displacement of the added vector components.
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