Energy

EnergyChapter 5 Section 2

What is Energy?

• Energy – A scalar quantity that is often understood as the ability for a physical system to produce changes on a different physical system.

• Units for energy is a “Joule”– The variable for a Joule is a capital “J”

Kinetic Energy

• Kinetic Energy – The energy of an object due to it motion.

• Kinetic energy depends upon the object’s velocity and mass.

• Any mass that is moving has kinetic energy.

Equation for Kinetic Energy

KE = ½mv²

Kinetic Energy = ½ x mass x (velocity)²

• Given the objects velocity and mass, the energy that the object has can be calculated using the formula above.

Example Problem

• A car traveling at 50m/s has a mass of 1000kg. Calculate the kinetic energy.

Example Answer

• KE = ½mv²

= ½ (1000kg) (50m/s) ²

=1,250,000

KE = 1,250,000J

Potential Energy

• Potential Energy – The energy associated with an object due to its position.

• In other words, potential energy is stored energy that has the potential to move because of its position with respect to some other location.

Different Forms of Potential Energy

• There are two different forms of potential energy:– Gravitational Potential Energy– Elastic Potential Energy

Gravitational Potential Energy

• Gravitational Potential Energy – Potential energy associated with an object due to its position relative to the Earth or some other gravitational source.

Gravitational Potential Energy Equation

PEg = mgh

Gravitational Potential Energy = mass x free-fall acceleration x height

Converting Gravitational Potential Energy into Kinetic Energy

• Imagine a rock falling off a cliff. As it falls, it gains kinetic energy since it picks up velocity as it falls to the ground below.

• But where does the kinetic energy come from?

• It comes from the gravitational potential energy that is associated with the rock’s initial position on the cliff relative to the ground below.

Origin of Gravitational Potential Energy

• Gravitational potential energy is a result of an object’s position, so it must be measured relative to some ZERO level.

• Doesn’t matter where you place the zero level (origin), but it must remain consistent through out the problem.

Example Problem

• How much potential energy does a rock have that has a mass of 10kg and is 100m off the ground on top of a cliff?

Example Problem Answer

• PEg = mgh

=(10kg)(9.8m/s²)(100m)

=9800J

PEg = 9800J

Elastic Potential Energy

• Elastic Potential Energy – The potential energy in a stretched or compressed elastic object.– Examples:

• Springs• Rubber bands• Shocks

Relaxed Length of a Spring

• The length of a spring when no external forces are acting on it is called the relaxed length of a spring.

• When an external force compresses or stretches a spring, elastic potential energy is stored in the spring.

Elastic Potential Energy Equation

PEelastic = ½kx²

Where:• Elastic Potential Energy – PEelastic

• k – Spring Constant

• x – Distance compressed or stretched

Spring Constant

• Spring Constant – A parameter that expresses how resistant a spring is to being compressed or stretched.

• For a flexible spring the constant is small and for a stiff spring the constant is large.

• The units for the spring constant is “N/m”

Example Problem

• A child has a rubber band with a length of 0.10m. The child pulls back on the rubber band to a distance of 0.20m. The spring constant of the rubber band is 5 N/m. What is the potential energy with in the rubber band?

Example Problem Answer

PEelastic = ½kx²

= ½ (k) (xf – xi)²

= ½ (5 N/m) (0.20m – 0.10m)²

= ½ (5 N/m) (0.10m)²

=0.025J

PEelastic = 0.025J

Mechanical Energy

• Mechanical Energy – The sum of kinetic energy and all forms of potential energy.– Example:

• Any kind of mechanical device– Clocks– Air compressor– Basically anything that has moving pieces…

– Doesn’t include electrical, chemical, or heat energy.

Mechanical Energy Equation

ME = KE + ΣPE

ME = Mechanical Energy

KE = Kinetic Energy

ΣPE = The sum of all the potential energy

Classification of Energy

Energy

Mechanical Non-mechanical

Kinetic Potential

GravitationalElastic