1. A plank of negligible weight 3.5 m long rests with one end on a rock and the other end on a scale. A woman is standing on the plank 1.0 m from the rock making the scale read 120 N. How much does the woman weigh?
To find out how much the woman weighs, we can use the concept of torque. Torque, defined as the product of force and distance from the axis, can help us solve this problem.
First, let's break down the given information:
Length of the plank (L) = 3.5 m
Distance of the woman from the rock (d) = 1.0 m
Reading on the scale (force exerted by the woman on the scale) = 120 N
Now, let's consider the equilibrium of torques around the point where the plank touches the rock:
The torque exerted by the woman's weight can be calculated as Torque = Force × Distance.
Since the woman's weight acts at the center of the plank (the middle point), the torque exerted by her weight is given by:
Torque from woman's weight = (weight of the woman) × (distance from the rock to the center of the plank)
Torque from woman's weight = (weight of the woman) × (L/2 - d)
Then, the total torque exerted on the plank is:
Total torque = Torque from woman's weight
In equilibrium, the total torque is zero, which means:
Total torque = 0
Setting up the equation:
(weight of the woman) × (L/2 - d) = 0
Now, we can solve for the weight of the woman:
(weight of the woman) = 0 / (L/2 - d)
Substituting the given values:
(weight of the woman) = 0 / (3.5/2 - 1.0)
(weight of the woman) = 0 / (1.75 - 1.0)
(weight of the woman) = 0 / 0.75
Since dividing by zero is undefined, it implies that the woman's weight is zero. This could mean that the woman is not standing on the plank, or the scale is not calibrated correctly.
Note: If we assume that the woman does have weight, then there may be an error in the calculation or an error in the given information.