Question

The two forces shown act on the member AB. Determine the magnitude of P such that the resultant of these forces is directed along AB.

Answer 1

Answer:

The resultant is formed by the vector addition of forces P and 5kN and must be in line with the bar (so that it is directed along AB).

This forms a parallelogram. We can use the sine rule on the triangle that is half the parallelogram:-

Answer 2

Answer:

The magnitude of P such that the resultant of these forces are directed along AB = 3.26kN

Explanation:

• A vector amount is described because of the bodily quantity that has both directions as well as magnitude.
• A vector with a value of magnitude identical to at least one is referred to as a unit vector and is represented via way of means of a lowercase alphabet with a “hat” circumflex i.e. “û“.

Examples of vector quantity include:

• Linear momentum
• Acceleration
• Displacement
• Momentum

CALCULATION:

The resultant is formed with the aid of using the vector addition of forces P and 5kN and should be in step with the bar (in order that it's far directed alongside AB).

This forms a parallelogram. We can use the sine rule at the triangle this is 1/2 of the parallelogram:-

P ÷ sin30=5 ÷ sin50

⇒P=0.5×5×1sin50 ≈ 3.26kN