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MrMuchimi
3 years ago
6

A 500 gram mass attached to a horizontal spring

Physics
1 answer:
Daniel [21]3 years ago
8 0
Is that a question? .
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The uniform slender bar AB has a mass of 6.4 kg and swings in a vertical plane about the pivot at A. If θ˙ = 2.7 rad/s when θ =
dolphi86 [110]

Answer:

F=√[(1.5(14.58L+11.96))² + (3.2(2.97L - 157.03) + 62.72)²]

Explanation:

Given data,

The mass of the bar AB, m = 6.4 kg

The angular velocity of the bar,  θ˙ = 2.7 rad/s

The angle of the bar at A, θ = 24°

Let the length of the bar be, L = l

The angular moment at point A is,

                        ∑ Mₐ = Iα

Where,     Mₐ - the moment about A

                 α  - angular acceleration

                 I - moment of inertia of the rod AB

                       -mg(\frac{lcos\theta}{2})=\frac{1}{3}(ml^{2})\alpha

                        \alpha=\frac{-3gcos\theta}{2l}

Let G be the center of gravity of the bar AB

The position vector at A with respect to the origin at G is,

                          \vec{r_{G}}=[\frac{lcos\theta}{2}\hat{i}-\frac{lcos\theta}{2}\hat{j}]

The acceleration at the center of the bar

                          \vec{a_{G}}=\vec{a_{a}}+\vec{\alpha}X\vec{r_{G}}-\omega^{2}\vec{r_{G}}

Since the point A is fixed, acceleration is 0

The acceleration with respect to the coordinate axes is,

                         (\vec{a_{G}})_{x}\hat{i}+(\vec{a_{G}})_{y}\hat{j}=0+(\frac{-3gcos\theta}{2l})\hat{k}\times[\frac{lcos\theta}{2}\hat{i}-\frac{lcos\theta}{2}\hat{j}]-\omega^{2}[\frac{lcos\theta}{2}\hat{i}-\frac{lcos\theta}{2}\hat{j}]

(\vec{a_{G}})_{x}\hat{i}+(\vec{a_{G}})_{y}\hat{j}=[-\frac{cos\theta(2l\omega^{2}+3gsin\theta)}{4}\hat{i}+(\frac{2l\omega^{2}sin\theta-3gcos^{2}\theta}{4})\hat{j}]

Comparing the coefficients of i

=-\frac{cos\theta(2l\omega^{2}+3gsin\theta)}{4}

Comparing coefficients of j

(\vec{a_{G}})_{y}=\frac{2l\omega^{2}sin\theta-3gcos^{2}\theta}{4}

Net force on x direction

F_{x}=(\vec{a_{G}})_{x}

substituting the values

F_{x}=1.5(14.58L+11.96)

Similarly net force on y direction

F_{y}=(\vec{a_{G}})_{y}+mg

               = 3.2(2.97L - 157.03) + 62.72

Where L is the length of the bar AB

Therefore the net force,

F=\sqrt{F_{x}^{2}+F_{y}^{2}}

F=√[(1.5(14.58L+11.96))² + (3.2(2.97L - 157.03) + 62.72)²]

Substituting the value of L gives the force at pin A

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Answer:

60

Explanation:

because it shows he is moving at a low speed

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<span>"In designing electrical circuits, it is important to know the characteristics of circuits in order to know how to solve related problems that will arise whenever there will be problems in the circuits made. For example, series circuits makes the other lights go off whenever one bulb does not work. It would be easier to determine how to fix it because we know what type of circuit it is."
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