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Later I will show you how to solve the same .problem mathematically which is probably the better choice for a blind student.
Now let's take another look at the same problem from a somewhat different graphical viewpoint. To recap, we have a point in a plane (the ring) which is subjected tothe following three vector forces and the ring is in equilibrium. (All angles are given relative to the positive horizontal axis).
We know that in order for the ring to be in equilibrium, the sum of the vectors for these three forces must add to zero. What are the magnitudes of theforces that vector B and vector C exert on the ring?
Drawing tail to tip
You learned in an earlier module that you can add vectors graphically by drawing them tail to tip. Once you have done that, the resultant vector is avector that extends from the tail of the first vector to the tip of the last vector.
Tactile graphics
The file named Phy1100d1.svg contains the image that is required to create a tactile graphic for this scenario.
Figure 10 shows the mirror image that is contained in that file for the benefit of your assistant who will create the tactile graphicfor this exercise.
| Figure 10 . Mirror image from the file named Phy1100d1.svg. |
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Figure 11 shows a non-mirror-image version of the same image.
| Figure 11 . Non-mirror-image version of the image from the file named Phy1100d1.svg. |
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Figure 12 shows the key-value pairs that go with the image in the file named Phy1100d1.svg.
| Figure 12 . Key-value pairs for the image in the file named Phy1100d1.svg. |
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m: Tip-to-tail force vector diagram
n: Vector Co: 7.3 newtons
p: 10 newtonsq: Vector A
r: 120 degreess: 45 degrees
t: File: Phy1100d1.svgu: Vector B
v: 5.3 newtons |
A closed path for equilibrium
For this case where the sum must be zero, the resultant vector must have a zero length. This means that the tip of the last vector must touch the tail ofthe first vector. In other words, the connected vectors must describe a closed path.
In the earlier modules, you were given the magnitude and direction of several vectors and you arranged them tail to tip in order to find the resultant vector.However, for this problem, you know the direction and magnitude of one vector but you only know the directions for the other two vectors. You need to findtheir magnitudes.
Knowing that the three vectors must form a closed path makes a graphical solution to this problem possible.
Draw a vector diagram
Begin by drawing vector A with a length of 10 newtons at an angle of -90 degrees, using whatever plotting scale works for you. The tail for this vectorwill be at the top of the vertical line and the tip will be at the bottom.
Add vector B to the diagram
Go to the tip of vector A and draw vector B with an unspecified length at an angle of 45 degrees. The tail of vector B will touch the tip of vector Aand the tip of vector B will be somewhere up and to the right of the tip of vector A.
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