My science teacher wants to know why cranes make work easier rather than just lifting an object yourself. She refers to the formula of force x distance. So i have to compare (in a way) the work of a human lifting an object and a crane lifting an object. Grrrr.... I hate this project!
The type of crane she is referring to ia a simple pole with a fulcrum placed between the person operating the crane, and the mass to be lifted. Imagine a weightless pole with a rope tied to one end attached to a mass of weight 224 lbs The pole is 9 feet long Let's say the human weighs 112 lbs, or half of what is to be lifted. Without a crane, it will be difficult to lift that much and swing it around. With the crane, though, let's look at the advantage when a fulcrum is placed under the pole and the person pushes down on the pole to lift the weight. First, note that gravity is in favor of the person to use their weight on the pole. Using physics, with the fulcrum place at x from the mass to be lifted, the downward force of the person is F*(9-x)=224*x or F=224*x/(9-x) now plug in some values for x and compute the force: x F 4.5 224 3.5 143 2.5 86 1.5 45 0.5 13 I started by placing the fulcrum exactly in the middle and then moving the fulcrum in increments of 1 foot closer to the weight to be lifted Notice that the more pole towards the person pressing down, the less force the person has to apply to lift the weight. Also, note that when the fulcrum is in the middle, the person must apply a downward force equal to the weight - which willl be difficult foir a person that weighs 112lbs. However, once the fulcrum is placed 2.5 ft from the weight, the person only need apply 86 lbs of downward pressure. Leverage. j
