In the last lesson we said that changes in momentum depended on a force and "how long" that force was applied. "How long" meant how much time. However, "how long" can also mean the distance through which the force is applied. We call the quantity produced by force and distance work. Work=force times distance, or W=Fd. So, if we lift a weight one meter up in the air, we do more work on that weight than if we had just lifted it half a meter up. If we push on a wall with 500 N of force, but the wall does not move, we have not done any work on the wall. Work requires a force and a distance.
The unit of measurement for work combines the force unit, the Newton, with the distance unit, the meter. This new unit, the N*M, we call a joule. The symbol for a joule is "j". So, if you lift a one Newton weight one meter, you have done one joule of work on the weight. 1N*1M=1j.
The definition of work says nothing about how long it takes to do the work. The same amount of work is done when we go up a flight of stairs, whether we walk or run. But we are more tired when we run up the flight of stairs. To understand this, we need to talk about a measure of how fast the work is done. This measure is called power. power is equal to the amount of work done per time it takes to do it. Power=work/time. The new unit for the measurement of power combines the joule and the second. J/s are called watts. So if I lift a 1N weight 1M in 1s, I have done 1W of power. 1N*1M/1s=1W.
When an archer pulls back on the bow string, he has done work on the bow. Now the bent bow has the ability to do work on the arrow, pushing it forward. Something has been acquired by the bow that allows it to do work on another object. This something is energy. Like work, energy is measured in joules. An object can have mechanical energy or potential energy.
An object may store energy because of it's position relative to another object. This type of energy is called potential energy. When a bow is drawn, energy is stored in the bow. The energy stored can later be transferred to the arrow. Work is required to elevate objects against earth's gravity. The potential energy of a body due to it's elevated position is called gravitational potential energy. The amount of gravitational potential energy possessed by an object is equal to the work done in lifting it. The work equal the force required to move it times the vertical distance it is moved. The force required to move it is equal to it's mass times the constant g. So gravitational potential energy =mass times g times height, or PE=mgh. The potential energy depends only on mg and h. The potential energy of an object at a ledge only depends on the height of the ledge, not the path taken to get the object onto the ledge.
If we push on an object, we can set it in motion. More specifically, if we do work on an object, we can change the energy of motion of the object. We call energy of motion kinetic energy. Kinetic energy depends on mass and speed. It is equal to one half the mass multiplied by the speed squared, or KE=1/2mv2. This means that if the speed of an object is doubled, it's kinetic energy is quadrupled. A car going at one hundred miles per hour skids four times as far as a car going at fifty miles per hour, because it has four times as much kinetic energy.
When a ball is thrown, work is done on it, giving it kinetic energy. The ball can then hit something and push it, doing work on the other object. Therefore we see that the kinetic energy of a moving object is equal to the work done in bringing it from rest to that speed. So, for initially stationary object, work=kinetic energy, or Fd=KE=1/2mv2. Looking further, we can see that for an object initially in motion, the work done on it is equal to it's change in kinetic energy. In this case Fd=
KE=1/2mv2.
Consider a ball on top of a large pole. The ball has a lot of potential energy. Now say that the ball is dropped. As the ball falls down, we see that it loses potential energy and gains kinetic energy, till at the bottom (right before hitting the ground) it has all kinetic energy. If we measure the changes in energy at several different places down the pole, we see that the kinetic energy of the ball and the potential energy of the ball always add up to equal the original energy of the ball. Energy is conserved.
Mouse Over to View AnimationA machine is a device for multiplying forces or simply changing the direction of forces. The principle underlying every machine is the conservation of energy concept. Consider the lever. As we do work on one end of the lever, the other end of the lever odes work on another object. If we push down, the load is lifted up. Our work input is equal to the levers work output. Winput=Woutput. Since work equals Fd, Fdinput=Fdoutput. If the pivot point, called the fulcrum, of the lever is close to the load being lifted, a small input force will produce a large out put force. This is because the input force is exerted through a large distance, and the load is moved through a short distance. So a lever can be a force multiplier, but it can't multiply work or energy. So the amount of work you do on one end of the lever is exactly equal to the amount of work done on the load.
A block and tackle, or system of pulleys, is also a simple machine that multiplies force at the expense of distance. One can exert a small force through a large distance and lift a heavy load through a short distance. Any machine that multiplies force does so at the expense of distance. Likewise, any machine that multiplies distance does so at the expense of force. No machine can do more output work than you do input work
Our previous examples were ideal machines. One hundred percent of the input work was turned into output work. In the real world, machines are not ideal machines. Work is turned into heat energy through friction, and the input work is more than the output work. Inefficiency exists whenever energy is transformed from one form to another. Efficiency can be expressed by the ratio Efficiency=useful energy output/total energy output, or E=Winput/Woutput
Kinetic energy and momentum are both properties of motion. But they are different. Momentum is a vector quantity, and energy is a scalar quantity. Another difference between energy and momentum is their proportionalities to velocity. Momentum is directly proportional to velocity, and energy is proportional to velocity squared. Consider a metal bullet fired into a block of wood. The bullet makes the wood tip over slightly as it penetrates into the wood. If the bullet is fired twice as fast, the block will tip twice as much. However, the bullet will penetrate four times as far. This is because the twice as fast bullet has four times as much kinetic energy while having only twice the momentum.
Mouse Over to View AnimationIf you are playing football, and a heavy man and a light man are running at you with the same momentum, which one would you rather have hit you? The heavy man! You will be knocked backwards the same distance by both of the players, since they have the same momentum, but you will be hurt more by the light player, who has a greater speed and therefore a much greater kinetic energy!