Mechanical Energy: Potential & Kinetic

Units of Energy The Joule is the unit of energy. 1 Joule = 1 kg x 1 m/s2 x 1 meter 1 J = 1 N x m Joules are part of the metric system as

use the same prefixes as grams, meters, and liters! (kilo-, centi-, milli-)

Example: 1000J = 1 kJ

Potential Energy

Energy that is stored as a result of position or shape.

1. Gravitational Potential Energy PEgrav The potential energy stored by

objects that are above the Earth’s Surface

PEgrav = (m)(Ag)(Δh) m = mass of object (kg) Ag = acceleration due to gravity

on Earth it equals 9.8 m/s2

Δ h = change in height of object (meters) Pegrav INCREASES

when an object is raised to a higher level

Example 1 A 5kg coconut is at the top of a 15m tree. What is

the potential energy of the coconut? Given:

m = 5kg g = 9.8 m/s2

Δh = 15m Unknown: PEgrav Equation: PEgrav = (m)(Ag)(Δh) Substitute: PEgrav = (5kg)x(9.8 m/s2)x(15m) Solve: PEgrav = 735 J

Example 2 A skier with a weight of 882N is at the top of a 130m

Olympic Ski Jump. What is the potential energy of the skier?

Given: Fw = 882N (hint: Fw =mAg) Δh = 130m

Unknown: PEgrav Equation: PEgrav = (Fw)(Δh) Substitute: PEgrav = 882N x 130m Solve: PEgrav = 114,660 J or 114.66kJ

2. Elastic Potential Energy

The potential energy of an object that is stretched or compressed. It springs back to its original shape

after it is stretched or compressed!Examples:

Stretching a rubber band Pulling a cello string Shock absorbers on a bike Air compressed when a basketball

bounces

Kinetic Energy

Kinetic Energy KE Energy of an object due to

motion Depends on mass & velocity

of object

Examples: Rollercoasters going downhill Skateboarding up and down a

half pipe Wind

KE = ½(m)(v2)

Example 1 Determine the kinetic energy of a 625-kg roller coaster

car that is moving with a speed of 18.3 m/s. G: mass is 625kg, velocity is 18.3 m/s

U: KE

E: KE=(1/2)(m)(v2)

S: KE=(1/2)∙(625kg)∙(18.3m/s)2

S: KE=104653.13J=1.05x105J

Example 2 If the roller coaster car in the previous

problem were moving with twice the speed, then what would be its new kinetic energy?G: mass is 635kg, velocity= 2∙18.3m/s=36.6m/sU: New kinetic energyS: KE=(1/2)(m)(v2)S: KE=(1/2)∙(625kg)∙(36.6m/s)2

S: KE=418612.5J= 4.19x105J

Identify Energy Transformations

Energy Conservation Energy can be converted from one form to

another. Energy cannot be created or destroyed. The gravitational potential energy of an object

is converted to kinetic energy as an object falls.

Mechanical Energy = KE+PE

Conservation of Mechanical Energy Calculation(KE+PE)beginning= (KE+PE)end

Example 1 Use the diagram to verify the conservation

of energy equation

Example 2

At a construction site, a 1.50kg brick is dropped from rest and hits the ground at a speed of 26.0m/s. Assuming air resistance can be ignored, calculate the gravitational potential energy of the brick before it was dropped? (Hint: Pegrav-before = KE-after)

KE = ½(m)(v2)