Question

If the equal tensions (t) in the pulley cable are 400 N, express in vector notation the force (r) exerted on the pulley by the two tensions. Determine the magnitude of r.

Answer 1

The force exerted on the pulley by two 400 N tensions at right angles to each other in vector notation is the vector sum of the tensions, and its magnitude is calculated using the Pythagorean theorem to be 566 N.

Step-by-step explanation:

If the equal tensions (t) in the pulley cable are 400 N, we express the force (r) exerted on the pulley by the two tensions in vector notation assuming the tensions act at right angles to each other, hence we use the Pythagorean theorem. Since the tensions are equal and the vectors are perpendicular, we can formulate the resultant force as:

r = √((400 N)² + (400 N)²)

To find the magnitude of r, we calculate:

|r| = √((400 N)² + (400 N)²) = √(160000 N² + 160000 N²) = √(320000 N²) = 566 N.

The pulley experiences a net force with a magnitude of 566 N due to the two tensions.