a bridge across a small stream is made by supporting a 10m long log with a mass of 75kg with ropes tied at the ends of the log to the tree on the banks. the rope on the right makes a 25 degree angle with the ground. the rope on the left makes a 20 degree angle with the ground. a 25kg child us standing 7.5 m from the left bank. write the net force equation for the y direction. write the net force equation for the x direction. write the torque equation (use the left end of the log as the axis of rotation).

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Asked Jun 13, 2019
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a bridge across a small stream is made by supporting a 10m long log with a mass of 75kg with ropes tied at the ends of the log to the tree on the banks. the rope on the right makes a 25 degree angle with the ground. the rope on the left makes a 20 degree angle with the ground. a 25kg child us standing 7.5 m from the left bank. write the net force equation for the y direction. write the net force equation for the x direction. write the torque equation (use the left end of the log as the axis of rotation).

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Expert Answer

Step 1

Let the mass of the log is M and the mass of the child is m. For y direction the torque equation is given by equation (1). The sum of forces acting along x and y direction will be zero.

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X 5 m 2.5m 2.5m 25° 200 mg 25x9.81 N Mg 75x9.81 N Figure 1

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Step 2

The equilibrium moment about left end of the log is zero.

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ΣΕ,-0 [for y direction T, sin 20° T, sin 25° = Mg + mg (1) ΣΗ-0 for x direction T cos 20° T, cos 25° (2)

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Step 3
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ΣΤ. =0 left end taking clockwise Mg x 5 mmg x 7.5m - T, sin 25 x10 0 (3) as positive direction

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Newtons Laws of Motion

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