I need help. I only have two attempts. Thank you! In the figure, a nonuniform ba

Question

I need help. I only have two attempts. Thank you!

In the figure, a nonuniform bar is suspended at rest in a horizontal position by two massless cords as shown in the figure here. One cord makes the angle ? = 41.0? with the vertical; the other makes the angle ? = 49? with the vertical. If the length L of the bar is 2.7 m, compute the distance x from the left end of the bar to its center of mass.

x=?

In the figure, a nonuniform bar is suspended at rest in a horizontal position by two massless cords as shown in the figure here. One cord makes the angle ? = 41.0? with the vertical; the other makes the angle ? = 49? with the vertical. If the length L of the bar is 2.7 m, compute the distance x from the left end of the bar to its center of mass. x=?

Explanation / Answer

Let the tension be T1 and T2 in left and right strings.

Force balance along x-axis

T1* sin 41 = T2 * sin49

T1/T2 = 1.15

T1 * cos41 + T2 *cos 49 = m*g

T2 *(1.15* cos41 +cos49) = m*g

T2 = m*g/1.524

Moment balance about left hand end of the bar

T2*cos(phi)* L = m*g*x

m*g*cos 49 * L/1.524 = m*g*x

x = L*cos49 = 2.7*cos49 /1.524= 1.162 m

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