Question

find the resultant of two forces a b at magnitude10n and 15n respectively acting at a point o at angle of55 also deduce the angle that the resultant forces makes with the components

Answer 1

To find the resultant of the two forces, we can use the parallelogram law of vector addition. Draw a parallelogram with sides representing the two forces, and the diagonal of the parallelogram represents the resultant force.

First, resolve the forces into their components. The component of force A acting along the x-axis is 10*cos(55°) = 5.66N, and the component along the y-axis is 10*sin(55°) = 8.09N. Similarly, the component of force B along the x-axis is 15*cos(55°) = 8.48N, and the component along the y-axis is 15*sin(55°) = 12.14N.

Now, add the components along each axis separately to get the components of the resultant force. The x-component of the resultant = 5.66N + 8.48N = 14.14N. The y-component of the resultant = 8.09N + 12.14N = 20.23N.

The magnitude of the resultant force = sqrt((14.14N)^2 + (20.23N)^2) = 24.29N.

To find the angle that the resultant force makes with the components, we can use the tangent function.

tan θ = (20.23N)/(14.14N) = 1.43

θ = tan^-1(1.43) = 54.2°

Therefore, the angle that the resultant force makes with the components is 54.2°.