Vector has a magnitude of 8.10 units and makes an angle of 52.0° with the positive x-axis. Vector also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods find the following.
a) The vector sum
Magnitude of A + B:___ units
Direction of A + B ____° counterclockwise from +x-axis
(b) The vector difference A - B.
Magnitude of A - B______ units
Direction of A -B_______° counterclockwise from +x-axis
a. 8.1[52o] + 8[180o]
X = 8.1*cos52 + 8*cos180 = 4.99 Units
Y = 8.1*sin52 + 8*sin180 = 6.38 Units.
Mag. = Sqrt(4.99^2+6.38^2 = 8.1 Units
tanA = Y/X = 6.38/4.99 = 1.27856
A = 51.97o = Direction.
b. 8.1[52o] - 8[180o]
Subtract and use same procedure as "a".
To find the vector sum A + B and the vector difference A - B using graphical methods, follow these steps:
1. Draw a coordinate system with the x-axis and y-axis.
2. Start by drawing vector A with a magnitude of 8.10 units and making an angle of 52.0° counterclockwise from the positive x-axis. Label it as A.
3. Next, draw vector B with a magnitude of 8.00 units and directed along the negative x-axis. Label it as B.
4. The vector sum A + B is obtained by placing the tail of vector B at the head of vector A, while maintaining their respective directions. Draw a line connecting the tail of A to the head of B. The resulting vector is the sum A + B.
5. Measure the magnitude of vector A + B using a ruler or scale. Record the result as the magnitude of A + B.
6. Measure the angle counterclockwise from the positive x-axis to the resultant vector A + B using a protractor. Record the result as the direction of A + B in degrees.
7. To find the vector difference A - B, first invert the direction of vector B. In this case, it means flipping it 180°. Label the inverted vector as -B.
8. Similar to step 4, place the tail of vector A at the head of vector -B. Draw a line connecting the tail of -B to the head of A. The resulting vector is the difference A - B.
9. Measure the magnitude of vector A - B using a ruler or scale. Record the result as the magnitude of A - B.
10. Measure the angle counterclockwise from the positive x-axis to the resultant vector A - B using a protractor. Record the result as the direction of A - B in degrees.
Now, let's use the graphical method to find the values for A + B and A - B.
a) The vector sum A + B:
- Measure the magnitude of A + B using a ruler or scale, and record the result as the magnitude of A + B in units.
- Measure the angle counterclockwise from the positive x-axis to the resultant vector A + B using a protractor, and record the result as the direction of A + B in degrees counterclockwise from the +x-axis.
b) The vector difference A - B:
- Measure the magnitude of A - B using a ruler or scale, and record the result as the magnitude of A - B in units.
- Measure the angle counterclockwise from the positive x-axis to the resultant vector A - B using a protractor, and record the result as the direction of A - B in degrees counterclockwise from the +x-axis.
By following these steps and using graphical methods, you can find the vector sum and difference of A and B.