An object experiences an acceleration of magnitude $3.75 m/s^2$. Calculat the mass of the object given there are three forces acting on an object as follows:

$\overrightarrow{F1} = (-2\overrightarrow{i}+ 2\overrightarrow{j})\; N$
$\overrightarrow{F2} = (5\overrightarrow{i}-3\overrightarrow{j})\; N$
$\overrightarrow{F3} = (-45\overrightarrow{i})\; N$

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• According to Newton's second law: When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
According to Newton's second law, $\large\Sigma $$F = \overrightarrow{F1} + \overrightarrow{F2} + \overrightarrow{F3} = m\overrightarrow{a} \Rightarrow \large\Sigma$$ F = (-2\overrightarrow{i}+ 2\overrightarrow{j})\; +(5\overrightarrow{i}-3\overrightarrow{j})\; + (-45\overrightarrow{i})\;$
$\Rightarrow \large\Sigma$$F =(-42\overrightarrow{i} -\overrightarrow{j})N \Rightarrow |\Sigma F| = \sqrt{F_x^2 + F_y^2} = \sqrt{42^2+1^2} = 42.012\;N \Rightarrow Mass = \large\frac{|\Sigma F|}{a}$$ = \large\frac{42.012\;N}{3.75 \;m/s^2}$$= 11.2032\;Kg$
edited Aug 19, 2014