A small girl of weight 150N is placed on the centre of the plank. She then walks to the right and goes past trestle Q. When the plank is on the point of tipping up, where will the fulcrum be?
To determine the position of the fulcrum when the plank is on the point of tipping up, we need to consider the balance of torques. Torque is the measure of how effectively a force can rotate an object about a particular axis. In this case, the axis is the fulcrum.
Let's analyze the situation step by step:
1. Determine the weight of the girl:
The weight of the girl is given as 150N.
2. Calculate the torque exerted by the girl:
The torque exerted by an object depends on the magnitude of the force and the distance from the fulcrum. The formula for torque is torque = force x distance (perpendicular to the line of action of the force).
Since the girl is at the center of the plank, the distance from the fulcrum to the girl is zero. Therefore, the torque exerted by the girl in this case is also zero.
3. Consider the tipping point:
As the girl moves to the right, the center of mass of the system (plank + girl) shifts to the right as well. The tipping point occurs when the torque exerted by the girl is balanced by the torque exerted by the weight of the plank. At this point, the plank is in equilibrium and can tip either way.
4. Calculate the torque exerted by the weight of the plank:
To find the torque exerted by the weight of the plank, we need to know the distance from the fulcrum to the center of mass of the plank, and the weight of the plank.
Let's assume the weight of the plank is W (in newtons) and the distance from the fulcrum to the center of mass of the plank is D (in meters).
The torque exerted by the weight of the plank is given by torque = force x distance.
Since the weight of an object is equal to the force it exerts due to gravity, we can rewrite the formula as torque = weight x distance.
5. Equate the torques and solve for the distance from the fulcrum:
At the tipping point, the torque exerted by the girl (0) is equal to the torque exerted by the weight of the plank (W x D).
Therefore, 0 = W x D.
Solving for D, we get D = 0.
This means that the fulcrum will be at a distance of zero from the center of mass of the plank when it starts to tip up.
In conclusion, when the plank is on the point of tipping up, the fulcrum will be right at the center of mass of the plank.