A mass of 25 kg is acted on by two forces: ₁ is 15 N due east, and ₂ is 10 N due north. The acceleration of the mass is

Question

Quizplus · Accepted Answer

First, we can determine the net force acting on the mass by using vector addition. We can draw a vector diagram where the 15 N force is represented by a vector pointing to the right (east) and the 10 N force is represented by a vector pointing up (north). The diagonal of the resulting parallelogram represents the net force.

Using the Pythagorean theorem, we can find the magnitude of the net force:

√(15² + 10²) = √325 ≈ 18 N

To find the direction of the net force, we can use trigonometry.

tanθ = (opposite/adjacent)

tanθ = 10/15

θ ≈ 33.7º north of east

Now we can use Newton's second law (F = ma) to find the acceleration:

a = F/m

a = 18/25

a ≈ 0.72 m/s²

So the acceleration is 0.72 m/s², and the direction is 33.7º north of east. Therefore, the answer is C.

A Mass of 25 Kg Is Acted on by Two