A thin rod of length 100cm is free to move in the x-y plane as shown. The forces

Question

A thin rod of length 100cm is free to move in the x-y plane as shown. The forces acting on the rod at a particular instant of time are shown in the figure. F1=5N acts at a distance d1=20 cm from O, F2=7 N at a distance d2=70cm, and F3 = 6N.

1) What is the magnitude of the net force on the rod? Express your answer to two significant digits.

2) Using the figure, calculate the magnitude of the net torque about axis passing through the point O along the zz-axis. Express your answer to two significant digits.

3) What is the magnitude of the net torque about an axis passing through the midpoint ( x =50) of the rod (instead of point O) along the z-axis?

Explanation / Answer

1) Fnet = F3 i + (F2 - F1) j

= 6 i + 2 j

magnitude = sqrt(6^2 + 2^2) = 6.3 N

2) torque = (0.70 x 7 x sin90) - (0.20 x 5 x sin90)

= 3.9 N m

3) torque = ((0.70 - 0.50) (7) ) + ((0.50 - 0.20) (5))

= 2.9 N m

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