Answer to Question #116943 in Mechanics | Relativity for samantha

Question

Two forces of magnitudes 6.0N 4.0N act on a 3.2kg body. What is the acceleration produced when these forces are acting in the same direction? What is the acceleration produced when these forces are opposite directed? Draw the Free Body Diagram for each

Answer 1

Let's draw the free body diagram for the first case,

Suppose, $F_1=4N$ and $F_2=6N$ ,thus from the free body diagram the net force acting on $m=3.2Kg$ is

$$F_{net}=F_1+F_2\\ \implies F_{net}=4+6=10N$$

Now, from Newton's second law,

$$F_{net}=ma$$

where, $a$ is the acceleration of the object $m.$ Hence,

$$10=(3.2)a\implies a=\frac{25}{8}ms^{-2}$$

in the rightward direction.

Now, suppose the force acting on the mass $m$ is in opposite direction,thus free body diagram will be,

Hence, net force acting on $m$ is

$$F_{net}=F_2-F_1\implies F_{net}=2N$$

Again by applying Newton's second law we get,

$$ma=F_{net}\\ a=\frac{5}{8}ms^{-2}$$

in the direction of $F_2$ force i.e rightward direction.