An object with a mass of $9 k g$ $9 kg$ 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?

Question

An object with a mass of $9 k g$ $9 kg$ 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?

1 Answer

Impact of this question

1911 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-23T02:51:38

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

Explanation:

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

$F_{tot} = \sum F_{i}$ $F_"tot"=sumF_i$

In this case

$F_{tot} = F_{1} + F_{2}$ $F_"tot"=F_1+F_2$

Then adding algebraically we get

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

$= < 6 N, - 4 N >$ $= <6N,-4N>$

and by Newton's 2nd Law

$F = m a$ $F=ma$

Then we divide by $m = 9 k g$ $m=9kg$

$F_{tot} = 9 k g \cdot < \frac{2}{3} \frac{m}{s^{2}}, - \frac{4}{9} \frac{m}{s^{2}} >$ $F_"tot"=9kg*<2/3m/s^2,-4/9m/s^2>$

Then

$a = < \frac{2}{3} \frac{m}{s^{2}}, - \frac{4}{9} \frac{m}{s^{2}} >$ $a=<2/3m/s^2,-4/9m/s^2>$

The rate of acceleration is the magnitude of a.

$| a | = \sqrt{{(\frac{2}{3})}^{2} + {(- \frac{4}{9})}^{2}} = \sqrt{\frac{4}{9} + \frac{16}{81}} = \sqrt{\frac{36}{81} + \frac{16}{81}} = \sqrt{\frac{52}{81}} = \frac{4 \sqrt{13}}{9} \approx 1.602 \frac{m}{s^{2}}$ $|a|=sqrt((2/3)^2+(-4/9)^2)=sqrt(4/9+16/81)=sqrt(36/81+16/81)=sqrt(52/81)=(4sqrt(13))/9approx1.602m/s^2$

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

$θ = arctan (- \frac{2}{3}) \approx . - 0.588 r a d \approx - {33.69}^{\circ}$ $theta=arctan(-2/3)approx.-0.588 radapprox-33.69^@$

Science

Math

Humanities

... and beyond

An object with a mass of $9 k g$ $9 kg$ 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?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

An object with a mass of 9kg9 kg is acted on by two forces. The first is F1=<−2N,−1N>F_1= < -2 N , -1 N> and the second is F2=<8N,−5N>F_2 = < 8 N, -5 N>. What is the object's rate and direction of acceleration?

1 Answer

Explanation:

Related questions

Impact of this question

An object with a mass of $9 k g$ $9 kg$ 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?