Kinetic and Potential Energy Notes Chapter 5-2

Mechanical Kinetic Energy

• • • • Amount of energy an object has based on motion Depends on the mass of the object and its speed Kinetic Energy = ½ mass x velocity 2 – KE = ½ mv 2 Units of Energy– (kg) (m/s) 2 or kg m – Same as unit for work—Joules (J) 2 / s 2

• A 1400 kg car moving at a velocity of 18 m/s has what amount of Kinetic Energy?

• How fast would a basketball with a mass of 2.3 kg have to go to have the same amount of kinetic energy as the above car?

Work – Kinetic Energy Theorem

• • The amount of work done on an object can be translated into movement of the object Work can be related to the change in the kinetic energy of the object – Called the Work-Kinetic Energy Theorem – Work = ∆ Kinetic Energy • W = ∆ KE

Potential energy is stored energy --the energy is not being used now but could be used in the future --2 types: gravitational potential energy (PE g ) elastic potential energy (PE e )

Gravitational potential energy

• the energy an object has based on position – depends on its mass, gravity, and its height above a reference point – gravity is trying to pull the object back down to the earth • Ex: apple on a tree, skier atop a hill, rock on cliff, etc.

Gravitational potential energy formula

Potential energy = mass x gravity x height PEg = mgh (F x d where F = mg and d = h) --units of Joules (kg x m/s 2 x m) – Height is measured from a reference point • • Usually the ground or the surface beneath the object Can lead to a negative height – Ex. An object under water or below ground, any object below the reference point

Sample problems

• How much potential energy does a 55 g apple have hanging 3.5 meters high in a tree?

• A 55 kg skateboarder is at the top of a ramp with a slope of 35 degrees. The ramp is 5.5 m long. How much potential energy does the person have?

Elastic Potential Energy

--the amount of energy in a stretched or compressed object --a stretched rubber band, a stretched spring, a compressed golf ball http://www.youtube.com/watch?v=2Y57pw_iWl k

• the energy comes from the molecules wanting to return to their “normal” state – in stretching or compressing, the molecules get pushed closer to or pulled further from their neighboring molecules.

– the energy comes from the attraction or repulsion of the molecules to return to their “relaxed” position

• • amount of energy is based on the strength of the spring or stretched object and the distance it is stretched the spring constant (k) measures the strength of the spring or elastic object – the stronger the spring, the higher the k value – the farther the spring or elastic object is stretched, the greater strain on the molecules  the more potential energy

Elastic potential energy formula

• potential energy = ½ x spring constant (k) x distance from relaxed state 2 PEe = ½ k x 2 --the spring constant has units of (N/m) so the units become (N/m) x m 2 which reduces to N x m or Joules (J)

Sample elastic potential problems

• A person jumping on a pogo stick compresses a spring with a spring constant of 9800 N/m a distance of 15 cm. How much energy is stored in the spring?

• A slingshot has a normal length of 26.0 cm. A person puts a marble in it and pulls it back to a length of 54.5 cm. The spring constant is 350 N/m. Find the energy of the rubber band.