Final answer:
The woman can walk up to 1.3125 meters from the wall edge before the plank begins to rotate. This is determined by balancing the torques due to the weight of the plank and the woman's weight, which should be equal for the plank not to tip.
Step-by-step explanation:
The question involves a uniform wooden plank with a length of 5m and a mass of 75kg. The plank is placed on a brick wall so that 1.5m of it extends beyond the edge. The goal is to determine how far a 100kg woman can walk on the plank before it begins to rotate, with the axis of rotation being the edge of the wall.
To solve this, we have to consider the plank in static equilibrium, where the torque produced by the woman's weight is balanced by the torque produced by the weight of the plank acting at its center of gravity. The formula for torque (τ) is τ = force (f) times the lever arm (distance from axis of rotation, r), or τ = f * r.
Firstly, the torque produced by the weight of the plank only is about the edge of the wall:
- Weight of the plank, Wp = mg = 75kg * 9.8m/s2
- Distance to the center of gravity of the plank from the wall edge, rp = (5m-1.5m)/2 = 1.75m
- Torque due to plank's weight, τp = Wp * rp
Next, the torque produced by the woman's weight (assuming the plank is just about to tip, and the woman is at distance x from the wall edge):
- Weight of the woman, Ww = 100kg * 9.8m/s2
- Distance to the point of rotation, rw = x
- Torque due to woman's weight, τw = Ww * rw
For the plank not to rotate, these torques must balance out:
- τp = τw
- Wp * rp = Ww * rw
- (75kg * 9.8m/s2 * 1.75m) = (100kg * 9.8m/s2 * x)
- x = (75 * 9.8 * 1.75) / (100 * 9.8)
- x = 1.3125m
Therefore, the woman can walk up to 1.3125m from the wall edge before the plank begins to rotate, making 1.3125m the correct option.