Answer to Question #347099 in Physics for Oni chan

Question

Three forces F1 , F2 , and F3 act on an object with mass 25 kg.

The forces are the following:

F1 = 3i 6j + 3k

F2 = 5i + 9j + 2k

F3 = 6i + 3j - 6k ,

where the forces are measured in Newtons. (a) What is the net force vector? (b) What is

the magnitude of the net force? (c) What is the acceleration vector? (d) What is the

magnitude of the acceleration vector?

Answer 1

(a) the net force

$$\vec F=\vec F_1+\vec F_2+\vec F_3\\ = (3i+6j + 3k)\!+\!(5i + 9j + 2k)\!+\!(6i + 3j - 6k) \\ =14i+18j-k$$

(b) the magnitude of a net force

$$F=\sqrt{14^2+18^2+(-1)^2}=23\:\rm N$$

(c) the acceleration vector

$$\vec a=\frac{\vec F}{m}=\frac{14i+18j-k}{25}=0.56i+0.72j-0.04k$$

(d) the magnitude of the acceleration

$$a=\frac{F}{m}=\frac{23}{25}=0.92\:\rm m/s^2$$