Kinetic & Gravitational Potential Energy Mechanical Energy Kinetic Energy Work-Energy Theorem Gravitational Potential Energy Energy is Conserved Energy Conservation Application Summary

Mechanical Energy Mechanical Energy is composed of both: Gravitational Potential Energy Kinetic Energy

Kinetic Energy (EK or KE) Kinetic energy is energy of motion When we do work on an object, energy is transferred into the system When the object gains energy, it begins to move If you do work on a car by pushing it, it gains kinetic energy and begins to move

Kinetic Energy Kinetic energy (Ek or KE) can be found using: EK is the kinetic energy of the object in joules, m is the mass of the object in kilograms, and v is the speed of the object in metres per second EK is a scalar quantity (no direction)

Kinetic Energy The energy of motion is called kinetic energy. The faster an object moves, the more kinetic energy it has. The greater the mass of a moving object, the more kinetic energy it has. Kinetic energy depends on both mass and velocity.

Kinetic energy is dependent upon the square of the speed. K.E. = ½ mass x v Kinetic energy is dependent upon the square of the speed. 2

Check Your Understanding Find the kinetic energy of a 48-g dart travelling at a speed of 3.4 m/s. Answer: 0.28 J

Check Your Understanding A 97-g cup falls from a kitchen shelf and shatters on the ceramic tile floor. Assume that the maximum kinetic energy obtained by the cup is 2.6 J and that air resistance is negligible. What is the cup’s maximum speed? Answer: 7.3 m/s

Example #2 If a roller coaster car doubles it speed, how will that affect its Kinetic energy? What is the relationship between KE and velocity?

ANSWER If the speed doubles, the amount of KE will increase by 4. If the speed triples, then KE will increase by _____.

Work-Energy Theorem The total work done on an object equals the change in the object’s kinetic energy, provided there is no change in any other form of energy (for example, gravitational potential energy). We can summarize the relationship involving the total work and the kinetic energy as follows:

Check Your Understanding What total work, in megajoules (106), is required to cause a cargo plane of mass 4.55 x 105 kg to increase its speed in level flight from 105 m/s to 185 m/s? Answer: 5.28 x 103 MJ

Check Your Understanding A fire truck of mass 1.6 x 104 kg, travelling at some initial speed, has -2.9 MJ of work done on it, causing its speed to become 11 m/s. Determine the initial speed of the fire truck. Answer: 22 m/s

Gravitational Potential Energy (ΔEg or PE) The energy stored in an object due to its elevation above Earth’s surface The potential energy at a height “h” above that point is equal to the work which was required to lift the object to that height. Like charging a battery. You put energy into a battery which can be used at a later time.

Gravitational Potential Energy (ΔEg) Because gravity acts vertically, we will use h rather than Δd for the magnitude of the displacement. The force applied to the box to raise it is in the same direction as the displacement and has a magnitude equal to mg. Therefore, the work done by the force on the box is W = mgh Since the energy obtained at the top is equal to the work it took to get there W = ΔEg = mgh

Things to keep in mind ΔEg = mgh ΔEg = the change in potential energy from one height to another ΔEg is the change in gravitational potential energy, in joules; m is the mass, in kilograms; g is the magnitude of the gravitational field constant in m/s2; and h is the vertical component of the displacement, in metres. ΔEg = mgh

Check Your Understanding A diver, of mass 57.8 kg, climbs up a diving board ladder and then walks to the edge of the board. He then steps off the board and falls vertically from rest to the water 3.00 m below. Determine the diver’s gravitational potential energy at the edge of the diving board, relative to the water. Answer: 1.70 x 103 J

Check Your Understanding In the sport of pole vaulting, the jumper’s centre of mass must clear the pole. Assume that a 59-kg jumper must raise the centre of mass from 1.1 m off the ground to 4.6 m off the ground. What is the jumper’s gravitational potential energy at the top of the bar relative to where the jumper started to jump? Answer: 2.0 x 103 J

Check Your Understanding A 485-g book is resting on a desk 62 cm high. Calculate the book’s gravitational potential energy relative to the desktop and the floor. Answer: a) 0 J b) 2.9 J

Check Your Understanding The elevation at the base of a ski hill is 350 m above sea level. A ski lift raises a skier (total mass = 72 kg, including equipment) to the top of the hill. If the skier’s gravitational potential energy relative to the base of the hill is now 9.2 × 105 J, what is the elevation at the top of the hill relative to sea level? Answer: 1.7 x 103 J

Energy is Conserved Energy cannot be created or destroyed, only converted from one form to another Work is done to move an object upwards giving it Ek (because it is moving) and Eg (because it is gaining height) Once v = 0 the object stops moving up and Ek = 0. The energy from EK is completely converted to Eg at its peak Once the objects starts to descend, Eg is converted to EK as the objects gains speed

Energy Is Conserved If you raise an object to the top of a hill, you are giving it potential energy (Eg) As the object moves down the hill, it converts its potential energy into kinetic energy As kinetic energy increases, speed increases. This is why the object will be going faster at the bottom of the hill then at the top

Application Hydroelectric plants convert the Eg of the water at higher elevations into EK as water rushes down via gravity to spin turbines to create electricity

Summary Kinetic energy (EK): The energy of motion Gravitational Potential Energy (ΔEg): The energy stored in an object due to its elevation above a reference point Energy can be converted from one form to another (i.e. EK to Eg) Mechanical energy is the sum of potential energy and kinetic energy. It is the energy associated with the motion and position of an object. Example: If EK = 100 J and Eg = 50 J. What is the mechanical energy of the system. Answer: 150 J