For Questions 5, 6, and 7, use the following values:
A~ = 5.0 N at 135.0
◦ B~ = 6.0 N at 270.0
◦
If you get the same answer for Questions 5 and 6, ask for help!
5. Using the component method, add vectors A~ and B~ (i.e., R~ = A~ + B~ ).
6. Using the component method, add vectors A~ and −B~ (i.e., R~ = A~ − B~ ).
7. Using the Tail-to-Head method, add vectors A~ and B~ (R~ = A~ + B~ ), on the back of this sheet; rulers and
protractors will be provided in the physics building. Let 2.0 cm = 1.0 N.
To solve Questions 5 and 6, we can use the component method which involves breaking down each vector into its respective x and y components and then adding or subtracting these components to find the resultant vector.
For Question 5, we need to add vectors A~ and B~. Given:
A~ = 5.0 N at 135.0°
B~ = 6.0 N at 270.0°
Step 1: Resolve vector A~ into its x and y components.
Ax = A * cos(θ)
Ay = A * sin(θ)
In this case, A = 5.0 N and θ = 135.0°:
Ax = 5.0 N * cos(135.0°)
Ay = 5.0 N * sin(135.0°)
Step 2: Resolve vector B~ into its x and y components.
Bx = B * cos(θ)
By = B * sin(θ)
In this case, B = 6.0 N and θ = 270.0°:
Bx = 6.0 N * cos(270.0°)
By = 6.0 N * sin(270.0°)
Step 3: Add the x and y components of both vectors to find the resultant vector.
Rx = Ax + Bx
Ry = Ay + By
Step 4: Calculate the magnitude and angle of the resultant vector using the Pythagorean theorem and inverse tangent function.
R = sqrt(Rx^2 + Ry^2)
θ_R = atan(Ry / Rx)
Do the same steps for Question 6, but for vector -B~ instead of B~.
If you get the same answer for Questions 5 and 6, it indicates an error. In that case, consider reviewing the calculations or seeking help from an instructor or classmate to identify and resolve the issue.
For Question 7:
Using the Tail-to-Head method involves drawing the vectors to scale and placing the tail of one vector at the head of the previous vector, forming a chain. We will use a scaling factor of 2.0 cm = 1.0 N.
1. Draw a line to represent vector A~. Label its magnitude and angle.
2. Using a ruler and protractor, measure and draw vector B~ starting from the head of vector A~. Label its magnitude and angle.
3. Measure the magnitude and angle of the resultant vector, R~.
4. Convert the measured magnitude of R~ into Newtons using the scaling factor. (e.g., If the magnitude of R~ is measured as 4 cm, then R = 2.0 N)
5. Calculate the angle θ_R between the positive x-axis and R~ using the protractor measurement.
6. Label the magnitude and angle of R~ on the diagram.
Remember to use the provided rulers and protractors to ensure accurate measurements.