An object with a mass of $3 k g$ $3 kg$ is acted on by two forces. The first is $F_{1} = < - 2 N, - 5 N >$ $F_1= < -2 N , -5 N>$ and the second is $F_{2} = < 7 N, 3 N >$ $F_2 = < 7 N, 3 N>$ . What is the object's rate and direction of acceleration?

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Answer 1 · 2016-08-19T23:26:33

rate : $\frac{\sqrt{29}}{3} m / s^{2}$ $sqrt 29/3 m "/" s^2$

direction : $arctan (- \frac{2}{5})$ $arctan (-(2)/(5))$

$Sigma vec F = m vec a$

Here

$Sigma vec F = ((-2),(-5)) + ((7),(3)) = ((5),(-2)) = color(red)(m vec a)$

$implies ((5),(-2)) = 3 ((a_x),(a_y))$

$implies vec a = 1/3((5),(-2))$

$abs(vec a) = 1/3 sqrt(5^2 + (-2)^2) = sqrt 29/3$

$tan varphi = (-2)/(5) implies varphi = arctan (-(2)/(5))$

An object with a mass of 3 kg3kg3 kg is acted on by two forces. The first is F_1= < -2 N , -5 N>F1=<−2N,−5N>F_1= < -2 N , -5 N> and the second is F_2 = < 7 N, 3 N>F2=<7N,3N>F_2 = < 7 N, 3 N>. What is the object's rate and direction of acceleration?