A uniform beam of mass M = 6.60 kg and length L = 12.0 m is resting on the point

Question

A uniform beam of mass M = 6.60 kg and length L = 12.0 m is resting on the point of a fulcrum as shown. The fulcrum point is situated a distance d = 4.80 m from the left end of the beam. Mass m1 = 11.5 kg is attached to the beam a distance x1 = 1.80 m to the left from the fulcrum point. Mass m2 is attached to the beam a distance x2 = 6.40 m to the right from the fulcrum point.

a) Determine the magnitude of mass m2 by applying the conditions of static equilibrium for torque about a chosen convenient pivot point. Arrive at one equation which you can solve for this mass.

b) Determine the magnitude of the normal force of the fulcrum point on the beam by applying the conditions of static equilibrium for forces in the vertical direction to arrive at an equation containing all the vertical forces acting on the beam

Explanation / Answer

a)

Here , for the rod to be in static equilibro=ium

the net momentum about the fulcrum will be zero

balancing the momentum about fulcrum

1.8 * (11.5) * g - (6 - 4.8) * 6.6 * g - 6.4 * m2 * g = 0

1.8 * (11.5) - (1.2) * 6.6 - 6.4 * m2 = 0

solving for m2

m2 = 2 kG

the mass me is 2 Kg

b)

Normal force at the fulcrum

for the net forces in vertical direction to be zero

N1 - m1 * g - m2 * g - M * g = 0

N1 = (6.6 + 2 + 11.5) * 9.8

N1 = 197 N

the magnitude of the normal force of the fulcrum point on the beam by applying the conditions of static equilibrium is 197 N

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