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NRG Stored and moving, not measured the same. NRG There are two forms of energy that we deal with on the planet earth everyday. They are : Potential Energy Kinetic Energy 1 Potential Energy: Energy that is stored due to the position of an object. This position is in relation to a reference or zero point. Because of this, NRG is stored by doing work against another force. Gravitational Potential Energy • Energy stored in an object due to its position above the ground. Work is done against gravity and stored in the new position of the body. • The ground is used as a reference point for measurements. Height Ground is where Potential NRG can be zero 2 Work is done against gravity and stored in the new position of the body. Height Ground is where Potential NRG can be zero If the body falls, the Potential NRG gained by doing work against gravity is regained by gravity as it does work. Potential NRG : PE Gravitational Potential NRG can be calculated. PE = mgh PE = Potential Energy m = mass in kilograms g = 9.8 m/s/s h = height of the object above the ground. 3 Gravitational Potential NRG Example 1 A book with a mass of 10 kg sits on a shelf 2 m above the ground. Find the potential energy for the book. Given : m = h= g = 9.8 m/s2 Equation : PE = mgh Solve : PE = NRG Kinetic Energy – The energy of motion. Any object with mass, that is in motion, has kinetic energy. If an object is not in motion, it does not have any kinetic energy. If the object does not have mass, it does not have any kinetic energy. 4 NRG Kinetic Energy Equation 2 KE = ½ mv Where KE = kinetic energy in J m = mass of the object in kg v = speed of the object in m/s The units of Kinetic Energy are Joules Energy Find the kinetic energy of a car with a mass of 300 kg traveling at 5 m/s. Given : m = v= 2 Equation : KE = ½ mv KE = KE = The car has a kinetic energy of _________ J 5 NRG Find the kinetic energy of a car with a mass of 300 kg traveling at 10 m/s. Given : m = v= Equation : KE = ½ mv2 KE = KE = What happened to the amount of kinetic energy as the velocity was doubled? NRG Any increase in mass causes the same increase in kinetic energy. From the previous example, when the speed doubled in size, the energy quadrupled. Why? Kinetic energy depends on mass and velocity. But the velocity component is squared. A change in velocity results in the NRG changing by the square of the change in how fast the body is moving. 6 Change in Kinetic Energy When the speed of a car is increased, the kinetic energy increases. A force is responsible for any change in velocity. That force acts over a displacement, so work is done by the force. Work done = change in kinetic energy W = KEf - KEi Change in Kinetic Energy For the car in our example The car went from having ____ J to _____ J of energy. Change in kinetic energy = _______J This was the work done by a force to accelerate the car from 5 m/s to 10 m/s. Work done = _________ J 7 Change in Kinetic Energy Looking at the results, does a doubling of the velocity equal a doubling of the kinetic NRG? ∆KE = 3750 J when the car goes from 0 m/s to 5 m/s. When the velocity is increased by 5 m/s to 10 m/s, ∆KE =11,250J Doubling the speed requires doing 3 times the work and the car will have 4 times the NRG. 8