An object with a mass of $6 k g$ $6 kg$ is acted on by two forces. The first is $F_{1} = < - 6 N, 2 N >$ $F_1= < -6 N , 2 N>$ and the second is $F_{2} = < 1 N, 3 N >$ $F_2 = < 1 N, 3 N>$ . What is the object's rate and direction of acceleration?

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An object with a mass of $6 k g$ $6 kg$ is acted on by two forces. The first is $F_{1} = < - 6 N, 2 N >$ $F_1= < -6 N , 2 N>$ and the second is $F_{2} = < 1 N, 3 N >$ $F_2 = < 1 N, 3 N>$ . What is the object's rate and direction of acceleration?

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Answer 1 · 2017-11-07T13:43:48

The rate of acceleration is $= 1.18 m s^{- 1}$ $=1.18ms^-1$ in the direction $= 135^{\circ}$ $=135^@$ anticlockwise from the x-axis.

Explanation:

The resultant force is

$\to F = {\to F}_{1} + {\to F}_{2} = < - 6, 2 > + < 1, 3 > = < - 5, 5 >$ $vecF=vecF_1+vecF_2=<-6,2> + <1,3> = <-5,5>$

The mass is $m = 6 k g$ $m=6kg$

According to Newton's Second Law of motion

$\to F = m \to a$ $vecF=mveca$

The acceleration is

$\to a = \frac{1}{m} \to F = \frac{1}{6} < - 5, 5 > = < - \frac{5}{6}, \frac{5}{6} >$ $veca=1/mvecF=1/6<-5,5> = <-5/6,5/6>$

The rate of acceleration is

$∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ ∣ ∣ < - \frac{5}{6}, \frac{5}{6} > ∣ ∣ ∣ ∣ ∣ ∣ = \sqrt{{(- \frac{5}{6})}^{2} + {(\frac{5}{6})}^{2}} = \sqrt{\frac{25}{36} + \frac{25}{36}} = \frac{\sqrt{50}}{6} = 1.18 m s^{- 2}$ $||veca|| =| |<-5/6,5/6>|| = sqrt((-5/6)^2+(5/6)^2)=sqrt(25/36+25/36)=sqrt50/6=1.18ms^-2$

The direction of acceleration is

$θ = arctan (\frac{\frac{5}{6}}{- \frac{5}{6}}) = arctan (- 1) = 135^{\circ}$ $theta = arctan((5/6)/(-5/6))=arctan(-1)=135^@$ antilockwise from the x-axis.

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An object with a mass of $6 k g$ $6 kg$ is acted on by two forces. The first is $F_{1} = < - 6 N, 2 N >$ $F_1= < -6 N , 2 N>$ and the second is $F_{2} = < 1 N, 3 N >$ $F_2 = < 1 N, 3 N>$ . What is the object's rate and direction of acceleration?

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Explanation:

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An object with a mass of 6 kg6kg6 kg is acted on by two forces. The first is F_1= < -6 N , 2 N>F1=<−6N,2N>F_1= < -6 N , 2 N> and the second is F_2 = < 1 N, 3 N>F2=<1N,3N>F_2 = < 1 N, 3 N>. What is the object's rate and direction of acceleration?

1 Answer

Explanation:

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An object with a mass of $6 k g$ $6 kg$ is acted on by two forces. The first is $F_{1} = < - 6 N, 2 N >$ $F_1= < -6 N , 2 N>$ and the second is $F_{2} = < 1 N, 3 N >$ $F_2 = < 1 N, 3 N>$ . What is the object's rate and direction of acceleration?