Calculate the resultant of five coplanar force of value,10N,12N,16N,20N,15Nacting on an object at 0

could be anything from 0 to 73N in any direction

yes

To calculate the resultant of coplanar forces, we need to find the sum of the forces in both the horizontal and vertical directions separately. Let's break down the given forces.

Horizontal Forces:
- The forces of 10N, 16N, and 15N are acting in the same direction.
- The forces of 12N and 20N are acting in the opposite direction.

Vertical Forces:
- There are no forces acting vertically according to the information given.

Now, let's calculate the resultant of the horizontal forces.

Horizontal Resultant:
= (10N + 16N + 15N) - (12N + 20N)
= 41N - 32N
= 9N

So, the horizontal resultant is 9N since the negative and positive forces in the horizontal direction cancel each other out.

To find the resultant force, we can use the Pythagorean theorem since there is no vertical force.

Resultant Force:
= √(Horizontal Resultant^2 + Vertical Resultant^2)
= √(9N^2 + 0^2)
= √(81N^2)
= 9N

Therefore, the resultant force acting on the object is 9N.

To calculate the resultant of coplanar forces, you need to find the vector sum of all the forces. Here's how to calculate the resultant of the five given forces:

1. Draw a coordinate system or simply use a piece of paper with a reference point O (0,0) in the center.
2. Choose a scale for the forces (e.g., 1 cm = 5N) and draw vectors representing the forces from point O in the appropriate directions.
3. Label each force vector with its value (10N, 12N, 16N, 20N, 15N).
4. Using a ruler and protractor, measure the length and angle (direction) of each force vector relative to a reference axis. Note that in this case, all the forces act in the same plane, so their directions are already coplanar.
5. Convert each force vector to its x and y components. To find the x-component, multiply the force magnitude by the cosine of the angle with the x-axis. To find the y-component, multiply the force magnitude by the sine of the angle with the x-axis.
6. Add up all the x-components and y-components separately.
7. The sum of the x-components will give you the x-component of the resultant force, and the sum of the y-components will give you the y-component of the resultant force.
8. Use the Pythagorean theorem to calculate the magnitude of the resultant force by taking the square root of the sum of the squares of the x-component and y-component.
9. Determine the angle of the resultant force with respect to the x-axis using the inverse tangent function (arctan) of the y-component divided by the x-component.

Once you apply these steps to the given forces, you should be able to find the magnitude and direction of the resultant force.