A mass of 25 kg is acted on by two forces, one of which is 15 N due east while the second one is 10 N due north. The acceleration of the mass is A) 0.72 m/ s², 56.3^o north of east. B) 0.20 m/ s², due east. C) 0.72 m/ s², 33.7^o north of east. D) 1.0 m/ s², 33.7^o north of east. E) 0.20 m/ s², 56.3^o north of east.

Question

Quizplus · Accepted Answer

First, we need to find the resultant force acting on the mass:
- Using Pythagorean theorem, the magnitude of the resultant force (F_r) is: 
F_r = sqrt((15 N)^2 + (10 N)^2) = 18.03 N
- Using trigonometry, the direction of the resultant force (theta) is:
theta = tan^-1 (10 N / 15 N) = 33.7 degrees north of east

Next, we can use Newton's second law to find the acceleration of the mass:
F_r = m*a
a = F_r / m
a = 18.03 N / 25 kg
a = 0.72 m/s^2

Finally, we need to find the direction of acceleration, which is the same as the direction of the resultant force:
The direction of acceleration is 33.7 degrees north of east.

A Mass of 25 Kg Is Acted on by Two