A body is under the action of two forces 8N, and 10N. Find the resistant of the forces if;the forces are parallel and act in the same direction
B)the forces are parallel and act in opposite direction.
C)the two forces are inclined at an angle of 60 degree to each other.
To find the resultant of forces acting on a body, we can use vector addition. The resultant force is the sum of the individual forces.
A) When two forces are parallel and act in the same direction:
In this case, the forces can simply be added together to find the resultant force.
Resistant force = 8N + 10N = 18N
B) When the forces are parallel and act in opposite directions:
In this case, we need to subtract the smaller force from the larger force.
Resistant force = |8N - 10N| = 2N (Since the direction of the force is opposite, we take the magnitude by ignoring the negative sign)
C) When the two forces are inclined at an angle of 60 degrees to each other:
In this case, we can resolve the forces into their components along the x-axis and y-axis.
Let's assume the 8N force is F1 and the 10N force is F2.
For F1 = 8N, the x-component (Fx1) is given by:
Fx1 = F1 * cos(60°) = 8N * cos(60°) = 8N * 1/2 = 4N
For F1 = 8N, the y-component (Fy1) is given by:
Fy1 = F1 * sin(60°) = 8N * sin(60°) = 8N * √3/2 ≈ 6.93N (rounded to two decimal places)
For F2 = 10N, the x-component (Fx2) is given by:
Fx2 = F2 * cos(60°) = 10N * cos(60°) = 10N * 1/2 = 5N
For F2 = 10N, the y-component (Fy2) is given by:
Fy2 = F2 * sin(60°) = 10N * sin(60°) = 10N * √3/2 ≈ 8.66N (rounded to two decimal places)
Now, calculate the x-components and y-components separately:
Fx_total = Fx1 + Fx2 = 4N + 5N = 9N
Fy_total = Fy1 - Fy2 = 6.93N - 8.66N ≈ -1.73N (rounded to two decimal places)
The resultant force can be obtained using the Pythagorean theorem:
Resistant force = √(Fx_total^2 + Fy_total^2) = √(9N^2 + (-1.73N)^2) = √(81N^2 + 3N^2) = √(84N^2) = √84N ≈ 9.16N (rounded to two decimal places)
Therefore, the resultant force when the two forces are inclined at an angle of 60 degrees to each other is approximately 9.16N.