physics question about a diving board?

Question

I'm tutoring a young lady in college level, algebra-based physics. The question asks her to find the total force applied on a diving board that is held in place by two mounts. The diving board is 5-meters long with a mass of 55 kg. The first mount is 3.4-meters from the water side of the diving board, the second mount is an additional 1.2-meters back (away from the water side). A person is standing on the edge of the board over the water, with a mass of 65 kg. The physics class has already studied the normal types of forces: gravity, Normal, friction (no friction is mentioned in the problem). This particular chapter is all about torque and inertia, so I'm sure the answer must include those. Any suggestions? Thanks!

Answer 1

The center mount acts as a fulcrum with only vertical force and reaction force. To find the force of the one that is 4.6 m from the water side , sum the torques about the mount acting as a fulcrum and set the sum equal to zero.
It isn't stated, so I will assume the board is of uniform mass. The center of mass of the board is 2.5 meters from each end. Also, use clockwise rotation as positive.

The torque of the mount, with force f
-f*1.2
The board
55*g*(3.4-2.5)
The person
65*g*3.4
sum and set equal to zero
65*g*3.4+55*g*(3.4-2.5)-f*1.2
simplify
g*(270.5)Nm=f*1.2
the force f is
g*225.4 N

If g=10, f=2254 N

The reaction force of the fulcrum can be found the same way
summing torque at the connection furthest away from the water now f is the reaction force of the fulcrum
f*1.2-55*g*(4.6-2.5)
-65*g*4.6=0

f=345.4*g
again, using g=10
f=3454 N

check by summing all of the vertical forces to see if they equal zero
g*225.4-345.4*g+55*g+65*g
it checks

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