Final answer:
The force exerted by pillar A on the diving board with an 82.0 kg diver standing at the edge is approximately 1066.3 N, determined by solving for equilibrium conditions and moments.
Step-by-step explanation:
To find the force exerted by pillar A on a light diving board supported by two pillars, we must consider the system in equilibrium. An 82.0 kg diver stands at the edge of a 5.00 m long diving board, where the two supports (pillars) are 1.60 m apart. We can solve this using the principle of moments (torque), where the sum of clockwise moments equals the sum of counterclockwise moments about any pivot point.
We will choose pillar B as our pivot point to simplify calculations. Let FA be the force exerted by pillar A, and let FB be the force exerted by pillar B. We can express the diver's weight as W = mg, where m is the diver's mass and g is the acceleration due to gravity (9.8 m/s2). Thus, W = 82.0 kg × 9.8 m/s2 = 803.6 N.
Since the diver is standing at the edge of the board (5.00 m from pillar B), and the weight of the diver acts at this point, and the distance from pillar A to pillar B is 1.60 m, we set up the equilibrium equation for torques:
Moments about B = 0
FA × 1.60 m = Weight × 3.40 m
Plugging in the known values:
FA × 1.60 m = 803.6 N × 3.40 m
FA = (803.6 N × 3.40 m) / 1.60 m
FA = 1706.08 N / 1.60 m
FA = 1066.3 N
Therefore, the force exerted by pillar A is approximately 1066.3 N.