Mechanical Energy: Potential & Kinetic

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Presentation transcript:

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

Energy that is stored as a result of position or shape. 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 Examples: 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/s U: New kinetic energy S: KE=(1/2)(m)(v2) S: KE=(1/2)∙(625kg)∙(36.6m/s)2 S: KE=418612.5J= 4.19x105J

Identify Energy Transformations

(KE+PE)beginning= (KE+PE)end 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)