flight -energy transformations gravitational into kinetic

Solution
The energy transformations of a coal fired power plant

Solar -------> Chemical potential --------> heat --------> kinetic----> electrical
Photosynthesis is the process that traps solar energy and converts it into chemical potential energy. This energy is stored in plant matter and is released as heat energy when coal is burnt. This heat is used to turn water into steam. The steam(water) molecules have a great deal of kinetic energy(they move very fast). This kinetic energy is used to turn the turbines that spin the generators producing electrical energy..

The energy transformations of a hydroelectric power plant

Solar-----> gravitational potential----->kinetic---->electrical

Water in the oceans of the world absorb solar heat energy. This heat energy causes the evaporation of many billions of tons of water around the world. The resultant water vapour rises high into the atmosphere where it condenses back into water and falls as rain. This water is trapped in man-made dams and used to turn huge turbines that spin the generators to create electrical energy.

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Energy transformations gravitational into kinetic
Heavy objects raised high above the ground contain a great deal of gravitational potential energy. As they are released, this energy often is converted into kinetic energy as the objects increase in speed as they fall. The law of Conservation of Energy states that "*Energy can not be created or destroyed"*. So that means that, in an ideal situation with 100% energy efficiency, all the gravitational potential energy is converted into kinetic energy as an object falls. The video on the right shows the energy of a wrecking ball and a water fall. Water raised to high levels can be used to ultimately generate electrical energy in hydro-electric powerstations. Lets work on some examples
A roller coaster is a classic example of conversion of kinetic energy into gravitational potential and gravitational potential into kinetic energy. Look at the animation on the right. We assume no energy is lost from the system. Notice how at the very top of the roller coaster the ball has all energy in the form of gravitational potential. As it falls gravitational energy is steadily converted into kinetic energy. At the bottom of the roller coaster all energy is in the form of kinetic energy. Notice in the animation on the right the total amount of energy is always constant, it just changes form. The ball has maximum speed at the bottom of the roller coaster. This is where all the potential energy is converted into kinetic energy. At the top of the roller coaster the ball is at its maximum height and therefore has maximum potential energy.

Example 1) A 400g cart sits 100m above the ground. It rolls off the edge and drops to ground level (point "A") along a roller coaster track. a) Calculate the kinetic and gravitational potential energies of the cart at point "A" The cart starts of with all its energy in the form of gravitational potential energy. mgh = 0.4 X 9.8 X 100 = 392 joules. As it rolls down the track gravitational potential energy is slowly converted to kinetic energy. At ground level (point "A") all the energy is now converted into kinetic and the expression below is true.


Click to see how the gravitational potential and the kinetic energies change. Since the height of the cart at "A" is zero its gravitational energy is zero. Since we have 100% conversion, the kinetic energy is equal to the gravitational potential energy the cart started with. Kinetic energy = 392 joules. b) What is the speed of the cart at point "A" Since all the energy is in the form of kinetic the expression below is true and we solve for "v".
v = 44.27 m/second
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