An object with a mass of 4 kg is acted on by two forces. The first is F_1= < -6 N , 3 N> and the second is F_2 = < 6 N, 5 N>. What is the object's rate and direction of acceleration?

Jun 8, 2016

The acceleration is $2$ $\frac{m}{s} ^ 2$ and the angle is ${90}^{\setminus} \circ$.

Explanation:

When you want to sum two vectors in classical mechanics, it is enough if you sum them component by component.

The final vector is

$F = {F}_{1} + {F}_{2} = < - 6 N + 6 N , 3 N + 5 N >$

$= < 0 N , 8 N >$

The length of a vector is given by

$L = \sqrt{{x}^{2} + {y}^{2}}$

that of our vector is

$L = \sqrt{{0}^{2} + {8}^{2}} = 8$.

Then the force is with a magnitude of 8N and the acceleration is given by

$F = m a$

$a = \frac{F}{m} = \frac{8}{4} = 2$ $\frac{m}{s} ^ 2$

The direction is given by

$\setminus \theta = \arctan \left(\frac{y}{x}\right) = \arctan \left(\frac{8}{0}\right)$

This of course is a problem because we cannot divide by zero. On the other hand we know that the arctan is singular when the angle is $\frac{\pi}{2}$. So the direction is an angle of $\frac{\pi}{2}$ or ${90}^{\setminus} \circ$.