A crowbar is of lengths 3m. Where should the fulcrum be placed along the length of the crowbar so that a boulder of 9kgwt be lifted with it by applying an effort of 10N.
If the fulcrum is placed at distance d from the weight, then the force*distance must match
(9*9.8)d = 10(3-d)
To solve this problem, we can use the principles of torque and lever arms. The torque generated by a force (effort) about a pivot point (fulcrum) is given by the formula:
Torque = Force * Lever Arm
The lever arm is the perpendicular distance between the line of action of the force and the pivot point. In this case, the lever arm is the distance from the fulcrum to the point where the boulder is attached to the crowbar.
Given:
Length of the crowbar (L) = 3m
Weight of the boulder (W) = 9kgwt (weight is a force and is typically measured in newtons, but we can use kgwt since it's common here)
Effort (Force applied) = 10N
First, let's calculate the lever arm for the weight of the boulder. Since the weight of the boulder acts vertically downward, the lever arm is the perpendicular distance from the fulcrum to the vertical line passing through the center of the boulder's mass.
We can assume that the weight of the boulder is concentrated at its central point. The center of mass of an object is typically also the point of balance. Therefore, the lever arm is half the length of the object.
Lever Arm = Length / 2 = 3m / 2 = 1.5m
Now, let's find the position of the fulcrum by using the formula for torque:
Torque = Force * Lever Arm
Since torque is equal to the lever arm multiplied by the force, we can rearrange the formula to find the position of the fulcrum:
Fulcrum position = Torque / Force
In this case, the torque generated by the weight of the boulder (W) is equal to the torque generated by the effort (10N):
W * Lever Arm = Effort * Fulcrum position
Substituting the given values:
9kgwt * 1.5m = 10N * Fulcrum position
Simplifying:
13.5kgwt m = 10N * Fulcrum position
Dividing both sides by 10N:
Fulcrum position = 13.5kgwt m / 10N
Simplifying:
Fulcrum position = 1.35m
Therefore, the fulcrum should be placed at a distance of 1.35m from one end of the crowbar in order to lift the 9kgwt boulder with an effort of 10N.