An object with a mass of $6 kg$ is acted on by two forces. The first is $F_1= < -1 N , 5 N>$ and the second is $F_2 = < 7 N, 3 N>$ . What is the object's rate and direction of acceleration?

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Answer 1 · 2017-02-21T14:12:40

The net acceleration is $=1.67ms^-2$ in the direction $=53.1$ º

The resultant force is

$vecF=vecF_1+vecF_2$

$= <-1,5>+<7,3>$

$=<6,8>$

$vecF=m veca$

$veca =1/m*vecF$

$=1/6<6,8> = <1, 4/3>$

The magnitude of the acceleration is

$||veca||=||<1,4/3>||$

$=sqrt((1)^2+(4/3)^2)$

$=sqrt(1+16/9)$

$=sqrt 25/3=1.67ms^-2$

The direction is $theta = arctan((4/3)/(1))$

The angle is in the 1st quadrant

$theta=arctan(4/3)=53.1$ º

An object with a mass of 6 kg6 kg is acted on by two forces. The first is F_1= < -1 N , 5 N>F_1= < -1 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?