An object with a mass of $9 kg$ is acted on by two forces. The first is $F_1= < -2 N , -1 N>$ and the second is $F_2 = < 8 N, -5 N>$ . What is the object's rate and direction of acceleration?

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Answer 1 · 2017-01-23T02:51:38

The object is accelerating at a rate of $1.602m/s^2$
at an angle of $-33.69^@$

The total force acting upon an object is the sum of all the forces acting on that object.

$F_"tot"=sumF_i$

In this case

$F_"tot"=F_1+F_2$

Then adding algebraically we get

$F_"tot"= <-2N,1N> + <8N,-5N>$

$= <6N,-4N>$

and by Newton's 2nd Law

$F=ma$

Then we divide by $m=9kg$

$F_"tot"=9kg*<2/3m/s^2,-4/9m/s^2>$

Then

$a=<2/3m/s^2,-4/9m/s^2>$

The rate of acceleration is the magnitude of a.

$|a|=sqrt((2/3)^2+(-4/9)^2)=sqrt(4/9+16/81)=sqrt(36/81+16/81)=sqrt(52/81)=(4sqrt(13))/9approx1.602m/s^2$

The direction is down and to the right and the angle $theta$

$theta=arctan(-2/3)approx.-0.588 radapprox-33.69^@$

An object with a mass of 9 kg9 kg is acted on by two forces. The first is F_1= < -2 N , -1 N>F_1= < -2 N , -1 N> and the second is F_2 = < 8 N, -5 N>F_2 = < 8 N, -5 N>. What is the object's rate and direction of acceleration?