Answer:
see attached for a diagram and loads
Step-by-step explanation:
The mass of the man represents a downward force of ...
F = ma
F = (85 kg)(9.8 m/s²) = 833 N
at a point 1.5 meters from one support. In the attached diagram, the man is standing left of center, so is 1.5 m from the left support, and 4.9 m from the right support.
The mass of the beam represents a downward force of ...
F = (15 kg)(9.8 m/s²) = 147 N
This is effectively modeled by a force acting on the center of the beam, 3.2 m from each support. The distance between supports is 6.8 -2(0.2) = 6.4 m.
The net torque on the beam is zero. This means we can sum the torques at either support and set them to zero. If we let s1 represent the upward force supplied by the left pillar, and s2 the upward force supplied by the right pillar, the two torque equations are ...
torque = force × distance
CW torque about the left pillar: 833×1.5 +147×3.2 -s2×6.4 = 0
s2 = 1719.9/6.4 ≈ 268.7 . . . newtons
CCW torque about the right pillar: -s1×6.4 +833×4.9 +147×3.2 = 0
s1 = 4552.1/6.4 ≈ 711.3 . . . newtons
The magnitudes of the loads carried by the supports are 268.7 N and 711.3 N.
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Check
For static equilibrium, the sum of upward forces must match the sum of downward forces:
268.7 +711.3 = 980 . . . . newtons (total of upward forces)
883 +147 = 980 . . . . . . . newtons (total of downward forces)