Answer:
6.1 cm
61 N
35°
Explanation:
Given scale: 1 cm = 10 N
Question 6
Parallelogram method (attachment 1)
When two vectors are represented by two adjacent sides of a parallelogram by direction and magnitude, the resultant of these vectors is represented (in magnitude and direction) by the diagonal of the parallelogram starting from the same point.
F₁ = 30 N = 3 cm
F₂ = 40 N = 4 cm
Draw a 3 cm horizontal line from the head of vector F₂ that is parallel to and the same length as vector F₁.
Draw a 4 cm line from the head of vector F₂ that is parallel to and the same length as vector F₁.
You have now constructed a parallelogram.
The diagonal of the parallelogram represents the resultant force vector.
Measure the length of the diagonal:
- Resultant vector length = 6.1 cm
- Force represented by the length = 6.1 × 10 = 61 N
Measure the angle between the x-axis and the resultant force vector:
- Direction of resultant relative to x-axis = 35°
Question 7
Polygon method (attachment 2)
If a number of vectors can be represented in magnitude and direction by the sides of a polygon taken in the same order, then their resultant is represented in magnitude and direction by the closing side of the polygon taken in the opposite order.
F₁ = 30 N = 3 cm
F₂ = 40 N = 4 cm
Draw a 3 cm horizontal line from the origin along the x-axis. This is vector F₁.
Draw a 4 cm line at 60° to the x-axis from the head of F₁. The is vector F₂.
Close the polygon by drawing a line that connects the tail of vector F₁ to the head of vector F₂. This is the resultant force vector.
Measure the length of the closing side of the polygon:
- Resultant vector length = 6.1 cm
- Force represented by the length = 6.1 × 10 = 61 N
Measure the angle between the x-axis and the resultant force vector.
- Direction of resultant relative to x-axis = 35°
Note: The resultant vector length, force and direction are the same for both methods.
