course phys 241
vectors lab
Good work.
Force Vectors
For this experiment, I set up my board just as specified. The bottom rubber band had a length of 11.5 cm, giving it 2.31 N of energy. The left rubber band measured 9.6 cm, giving it an energy of 1.05 N. The right rubber band measured 10.4 cm, giving it an energy of 1.68 N.
I removed my rubber bands and drew my lines and coordinate plane. The point on the left was (-7,6.9). The point on the right was (3,9.8). The point on the bottom has the coordinates (0,-11.5) The angle of the point on the left is 134.59 degrees. The angle of the point on the right is 72.98 degrees. The angle of the bottom point is 270 degrees. Unfortunately, my points were not exactly 10 cm from the origin. Perhaps it was because the grid did not print proper, but my two lines were 9.6 cm and 10.4 cm from left to right, respectively.
My vector charts have three vectors, the one pointing up and to the left has a magnitude of 1.05 N. had the line been 10 cm as the experiment stated it should be, the magnitude would have been 1.3 N. The magnitude of the point to the right is 1.68 N, but once more, had my measurements been correct, the magnitude would have been 1.3 N. The vector pointing straight down has a magnitude of 2.31 N. The projection lines of the point to the left has a run of .75 cm, and a rise of .75 cm. the projection lines of the point to the right has a run of .5 cm, and a rise of 1.8 cm. These measurements would correspond to the left point having a vector on the x axis of .75 N, and .75 N on the y axis. The point on the right has a vector on the x axis of .5 N, and 1.8 N on the y axis. The following is a table of all raw data recovered.
Point 1 (top left) Point 2 (top right) Point 3 (bottom)
Distance from origin 9.6 cm 10.4 cm 11.5 cm
Distance on x-axis 7 cm 3 cm 0 cm
Distance on y-axis 6.9 cm 9.8 cm 11.5 cm
The next table is a length of each rubber band, and the Force of each.
Band 1 (top left) Band 2 (top right) Band 3 (bottom)
Length 9.6 cm 10.4 cm 11.5 cm
Force 1.05 N 1.68 N 2.31 N
This table shows the coordinates of the three points where the bands ended.
Band 1 (top left) Band 2 (top right) Band 3 (bottom)
Coordinates -7,6.9 3,9.8 0,-11.5
This table shows the length of each vector, the length of its components, and the Force of its components.
Point 1 (top left) Point 2 (top right) Point 3 (bottom)
Length of vector 1.05 cm 1.68 cm 2.31 cm
Length of x component -.75 cm .5 cm 0 cm
Length of y component .75 cm 1.8 cm -2.31 cm
Force of x component -.75 N .5 N 0 N
Force of y component .75 N 1.8 N -2.31 N
The total of all of my x components is -.25 cm. The total of all y components is .53 cm.
After connecting all vectors head to foot, there is a gap of .2 cm from the origin to the end of the third vector. The components of this vector are very close if not identical to the total of all of the components.
The magnitude and angle of the vectors are displayed in the following table.
Point 1 (top left) Point 2 (top right) Point 3 (bottom)
Length of vector 1.05 cm 1.68 cm 2.31 cm
Angle of vector 134.59 degrees 72.98 degrees 270 degrees
Length of x component .75 cm .5 cm 0 cm
Length of y component .75 cm 1.8 cm 2.31 cm
To find the length of the x and y components, I used trigonometry, specifically the Law of Sines to determine the length of one side of the triangle formed. After finding the length of the side, I used Pythagorean theorem to find the other side.
The sum of all of my x components is the same as the sum of all my x resultants.
The actual sum of all x components is -.25 N. The sum of all y components is .53 N. The resultant vector is where the vectors will send the object in the end. The magnitude of the vector is the force. The magnitude of my error is approximately 5%.
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