Calculate the resultant of five coplanar forces of values 10N,12N,16N,20N,15N acting on an object at 0
Magnitude and direction
yes
Not understood
Not undy
To calculate the resultant of five coplanar forces, we need to determine the vector sum of these forces. The resultant will give us both the magnitude (value) and direction of the net force.
To find the resultant:
Step 1: Decompose the forces into their horizontal and vertical components. This can be done using trigonometry. Since the forces are acting on the same plane, we can assume they are all acting in the same direction (e.g., horizontally or vertically).
Step 2: Add up all the horizontal components separately and calculate the vertical components separately.
Step 3: Combine the horizontal and vertical components to find the magnitude and direction of the resultant force using vector addition.
Let's break down these steps for your scenario:
Step 1: Decompose the forces
Since the forces are acting at 0 degrees (horizontal), we only need to consider the horizontal components of the forces. The horizontal component of a force can be calculated using the formula: Horizontal component = Force * cos(angle)
For the five forces:
Force 1: Horizontal component = 10N * cos(0) = 10N * 1 = 10N (no component in the vertical direction)
Force 2: Horizontal component = 12N * cos(0) = 12N * 1 = 12N (no component in the vertical direction)
Force 3: Horizontal component = 16N * cos(0) = 16N * 1 = 16N (no component in the vertical direction)
Force 4: Horizontal component = 20N * cos(0) = 20N * 1 = 20N (no component in the vertical direction)
Force 5: Horizontal component = 15N * cos(0) = 15N * 1 = 15N (no component in the vertical direction)
Step 2: Add up the horizontal components
Total horizontal component = 10N + 12N + 16N + 20N + 15N = 73N
Since all the forces are acting horizontally, there is no vertical component to calculate.
Step 3: Calculate the magnitude and direction of the resultant force
The magnitude of the resultant force can be found using the Pythagorean theorem:
Magnitude = sqrt((Total horizontal component)^2 + (Total vertical component)^2)
In this case, since there was no vertical component (all forces were acting horizontally), the magnitude of the resultant force is equal to the total horizontal component: Magnitude = 73N.
The direction of the resultant force is given by the angle it makes with the horizontal axis. In this case, since all forces are acting horizontally, the resultant force is also acting horizontally and parallel to the x-axis.
Therefore, the resultant of the five coplanar forces with values 10N, 12N, 16N, 20N, and 15N acting at 0 degrees is a force of 73N acting horizontally.