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 need to find the net force acting on the mass. We can use vector addition to do this:
Fnet = sqrt(F1^2 + F2^2 + 2*F1*F2*cos(theta))
where F1 and F2 are the magnitudes of the forces, and theta is the angle between them.

In this case, F1 = 15 N and F2 = 10 N, and they are at right angles to each other, so theta = 90 degrees.

Fnet = sqrt(15^2 + 10^2 + 2*15*10*cos(90))
Fnet = sqrt(325)
Fnet = 18.02 N

Now, we can use Newton's second law (F = ma) to find the acceleration:
a = Fnet/m
a = 18.02/25
a = 0.7208 m/s^2

Finally, we need to find the direction of the acceleration. We can use trigonometry to do this:
tan(theta) = F2/F1
theta = tan^-1(F2/F1)

theta = tan^-1(10/15)
theta = 33.69 degrees

Since the force in the east direction is greater than the force in the north direction, the acceleration vector will point somewhat northeast of due east. Therefore, the answer is C) 0.72 m/s^2, 33.7º north of east.

A Mass of 25 Kg Is Acted on by Two