Q4.2. A springboard-type diving board is built from high grade aluminum. This pa

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Q4.2. A springboard-type diving board is built from high grade aluminum. This particular board has a mass of 65 kg and is 3.85 m long, 33.8 cm wide, and 5 cm thick. (Aside: Most springboards start thick on one end, then get thinner as it moves to the other end. For this problem, assume the springboard has a constant thickness) One end of the springboard is attached to a hinge. The hinge lets the springboard move up and down, but keeps it from sliding out of place. 1.1 m away from the hinge, the springboard rests on (but is not attached to) a fulcrum. A diver with a mass of 65 kg stands on the far end of the springboard (opposite from the hinge), ready to begin their dive. Hinge Fulcrum Note: the measurements for this problem were taken from the springboards used in the 2016 Summer Olympics, 3 m Springboard event. Q4.3. What is the magnitude of the Torque on the board about the fulcrum due to the hinge? Answer in N·m 1270 2300 ×3700 Check Answer

Explanation / Answer

Since the system is in static equilibrium, the net torque about any point is zero.
Torque due to the weight of the spring board about the fulcrum, T1 = r1 x mg
r1 is the distance to the center of the spring board from fulcrum.
r1 = 3.85/2 - 1.1 = 0.825 m
m is the mass of the spring board, m = 65 kg

Torque due to the weight of the person standing at the edge of the spring board, T2 = r2 x Mg
r2 = 3.85 - 1.1 = 2.75 m
M = m = 65 kg

Consider the torque due to the hinge as Th
Net torque about the fulcrum = Th - (T1 + T2) = 0
Th = T1 + T2
= r1 mg + r2 Mg
= 0.825 x 65 x 9.8 + 2.75 x 65 x 9.8
= 2277 N m.

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