Mechanical energy is the energy which is applied to an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position).
Conservation of Energy
As with momentum, energy is conserved in all interactions. The Conservation law of energy said that energy can’t be created and can’t be demolished, but only can be changed into other form of energy. In the 20th centuries, this definition has been expanded to include mass because they both are in a same form.
In this page, we will only deal with mechanical energy. While the potential energy decrease, the kinetic energy increases, means the total energy (mechanical energy) remains same before and after.
TEbefore = TE after
For there, an object is not conserving the entire energy, but there is some energy loss. This energy is not destroyed, but changed into other form or absorbed by another object.
When you pull the weight at a constant velocity, approximately how much pulling force do you have to supply? (Here we can say only approximately, because there is some friction force involved in the pulleys. If the pulleys have weight then the pulling force will have an extra weight of the lower set of pulleys where the actual weight is attached.)
If you assume frictionless and weightless pulleys , when you pull with constant velocity, you can answer the question by counting the number of ropes on the lower pulley that support the weight. For instance, in Figure 2 there are four ropes that are holding up the weight, so the pull force that you have to supply is only 1/4 as much as the weight. However, if the rope is wound around only one set of reels as in activity 3, then the pulling force is only 1/2 as much as the weight.
Now if you attach the rope on the lower reel to start with as in Figure 4, then the pulling force is only 1/3 as much as the weight because only three ropes are supporting the weight. If you have more than two sets of reels, for example, use six reels arranged into three reels on each set as in Figure 5, then the pulling force is only 1/6 as much as the weight.
If you attach the top pulley to the ceiling, the ceiling will be pulled by the weight and the force you supply plus the weight of all the pulleys. Again you can count the number of ropes that are attached to the top pulley assembly plus the weight of all the pulleys, including both sets. For instance, in Figure 2 the ceiling is pulled with the weight plus 1/4 of the weight and the pulleys. In figure 3 the ceiling is pulled by the weight and 1/2 of the weight that you pull with and the weight of the pulleys.
How far is the weight lifted compared to how far down the pulling force has to travel? This question can be answered by the law of Conservation of Energy. In an ideal case, the pulleys are weightless and there is no friction between the rope and the reels, and the reels are completely free to turn, the work done to lift the weight equals the potential energy gained by the weight. The work done is the force you pull with multiplied by the distance you pull. So if you pull with 1/4 as much as the weight, the distance you pull down will be 4 times longer than the distance the weight is lifted up. (You can also reach the same conclusion by conservation of rope length. Just add up the lengths before lifting and after.)
You cannot save energy by using simple machines but you can save some force! In reality there is always friction, so you actually would do more work than the potential energy gained by the weight. The additional energy supplied by you will turn into heat through friction and also turns into the potential energy gained by the lower pulley assembly if it is not weightless.
If we consider the weight of the pulley assembly, the pulling force will now include pulling the attached weight and the bottom assembly pulley weight. Suppose the attached weight is W and the bottom pulley assembly weighs B, then the total weight that I have to pull is W + B. If again I use four pulleys, two in each set, as in Figure 2, then there are 4 ropes supporting the weight, my pull is 1/4 of the total weight of (W+B). The ceiling now has to support both the pull from the five attached ropes, 5/4 of the sum of the attached weight and the weight of the bottom pulley assembly, and the top pulley assembly weight. This is to say the ceiling supports 5/4 of (W+B) + Top pulley assembly. Similarly for the case of 6 pulleys as in Figure 5: there are six ropes supporting the attached weight, so my pulling force is 1/6 of the total weight of (W+B). The ceiling has to support 7/6 of (W+B) + the weight of the top pulley assembly. How far down the pulling force has to travel versus how far up the weight is lifted? Same answer as in the case for weighless pulley.
|Levers are mechanisms that can swivel or tip on a fixed point called a fulcrum. A see-saw is a lever. The fulcrum is in the middle of the see-saw and the people at each end can go up and down. |
In some levers the fulcrum is not in the centre but close to the end. A wheelbarrow has its fulcrum at the wheel which is at one end of the wheelbarrow.
For all levers, the force that makes it tip is called the effort. The thing that is being tipped is called the load.
There are three types of levers that are different in the order and direction of the load (L), effort (E) and fulcrum (F). The load is the weight we are trying to lift and the effort is the force we need to lift it. Whether we lift up or push down will depend on what we are trying to do. In the drawing opposite