Consider the situation illustrated below. The uniform 600 N beam is hinged at po

Question

Consider the situation illustrated below. The uniform 600 N beam is hinged at point P. The length of the beam is L. Find: a. The tension in the tie rope. b. The X component of the reaction force exerted by the hinge on the beam. c. The Y component of the reaction force exerted by the hinge on the beam. For the picture below let M = 1 kg, 2M = 2 kg and 3M = 3 kg. Also, let the distance (center to center) between the M and 3 M masses be 10 cm. Where should the middle mass (2M) be to experience a Net gravitational force of 0 (zero) Newtons due to the other two masses? Label the distance from respect of one of the other two masses.

Explanation / Answer

Force by M = Force by 3M

F = GM1M2/r^2

GM*2M/x^2 = G3M*2M/(0.1-x)^2

1/x^2 = 3/(0.1-x)^2

x^2 - 0.2x + 0.01 = 3x^2

2x^2 + 0.2x - 0.01 = 0

solving this quadratic equation

x = 0.0366 m = 3.66 cm from M

6.34 cm from 3M

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