G RAVITATIONAL AND P OTENTIAL E NERGY, AND K INETIC E NERGY Lesson 2

G RAVITATIONAL P OTENTIAL E NERGY (E G ) The type of energy that an object possess because of its position above some level. The energy is called potential because it can be stored and used at a lower level for work. When an object falls, its potential energy is transformed into kinetic energy as its speed increases.

K INETIC E NERGY ( E K ) Energy due to the motion of an object

G RAVITATIONAL P OTENTIAL E NERGY Since the force (F) required to lift an object without accelerating is the same as the objects weight (mg), the energy (E g ) required to lift an object is the same as its potential energy from the height it was lifted from. Since F = mg, we can make a common equation for gravitational potential energy. E g = F∆h = mg∆h, where g = 9.8 N/kg Energy is measured in joules and height is measured in meters.

The potential energy in a system must be based against a Reference Level – The level to which the object may fall. It is important to note that when answering questions about relative potential energy, it is important to state the reference level.

E XAMPLE 1 In the sport of pole vaulting, the jumper’s point of mass centralization, called the centre of mass, must clear the pole. Assume that a 59 kg jumper must raise the centre of mass 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 the point at which the jumper started the jump? h = 4.6 – 1.1 = 3.5 m m = 59 kg g = 9.8 N/kg E g = ?

E g = mgh E g = (59 kg) (9.8 N/kg) (3.5 m) E g = 2.0 x 10 3 J Therefore, the jumpers gravitational energy relative to the lower position is 2.0 x 10 3 J

K INETIC E NERGY Objects energy depends on two factors: 1. Mass 2. Speed The kinetic energy increases in direct proportion to the mass, and it increases in proportion to the square of the speed.

Where E K is the kinetic energy measured in joules (J) m is the mass in kilograms (kg) v is the speed in metres per second (m/s)

E XAMPLE 2 Find the kinetic energy of a 6.0 kg bowling ball rolling at 5.0 m/s m = 6.0 kg v = 5.0 m/s E k = ? E K = 75 J Therefore, the kinetic energy of the bowling ball is 75 J.

M ECHANICAL E NERGY The sum of gravitational potential energy and kinetic energy is called mechanical energy. E mechanical = E K + E g

When an object is raised to a position above a reference level, it contains the same amount of energy as it will at any point in the fall; the energy will just be in a different form. E k = E g

Q UESTIONS A o.45 kg book resting on a desktop 0.64 m high. Calculate the book’s gravitational energy relative to A) the desktop and B) the floor. T (2) ) 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) to the top of the hill, now the if the skiers gravitational potential energy relative to the base of the hill is 9.2 x 10 5 J, what is the elevation at the top of the hill? T (1)

Calculate the kinetic energy in each of the following; During a shot put, a 7.2 kg shot leaves the athletes hand at a speed of 12 m/s T (1) A 140 kg ostrich is running at 14 m/s T (1) A softball traveling at 34 m/s has a kinetic energy of 98 J. Calculate its mass. T(1)

A 1.0 kg object accelerates from a speed of 0.0 m/s to a speed of 5.0 m/s Determine the object’s kinetic energy at each of these speeds: 0.0 m/s, 1.0 m/s, 2.0 m/s, 3.0 m/s, and 4.0 m/s T (2) Draw a graph of the kinetic energy (vertical axis) as a function of speed. C (1) By what factor does the kinetic energy increase when the speed increases from 1.0 to 4.0 m/s? T (1) By what factor does the kinetic energy increase when the speed increases from 1.0 to 5.0 m/s? T (1)