KINETIC ENERGY ENERGY OF MOTION Kinetic Energy Two

KINETIC ENERGY: ENERGY OF MOTION

Kinetic Energy • Two things that determine an objects amount of kinetic energy is the objects mass and the speed of the object. • A softball travelling a 30 m/s has less kinetic energy than a bowling ball travelling at the same speed because the softball has less mass.

Observe the cyclist above moving her bicycle through a displacement d by applying a driving force F. The work that she does is given by the expression W = Fd v 1 = 0 Fd a Neglect friction Any object that is moving has kinetic energy. If you do work on an object causing it to move, you are transferring energy from your body into the object as kinetic energy.

• However the work that she does is converted to kinetic energy. Ek = Fd • According to Newton’s 2 nd law, F = ma Therefore Ek = mad • Recall that a = v – v 1 or since v 1 = 0 then a = v/t t • Also recall that d = (v 1 + v) t or since v 1 = 0, d = ½ vt 2 or simply Ek = ½ mv 2

• For example if the girl and her bicycle above had a combined mass of 120 kg and her final velocity was 8. 0 m/s, then the kinetic energy at the end would be • Ek = ½ mv 2 • = ½ (120 kg)(8. 0 m/s)2 • = (60 kg)(64 m 2/s 2) = 3840 J or 3. 8 x 103 J

• Example If a 0. 08 kg softball travels at 30 m/s determine its kinetic energy. • • Given (G): m = 0. 08 kg • Required (R): Ek • • Equation (E): Ek=1/2 mv 2 • Solution (S): = (0. 5)(0. 08 kg)(30 m/s)2 • =36 J • Statement (S): Therefore the kinetic energy of the softball was 36 J.

• Using the kinetic energy formula: rearrange the equation to find • a. m b. v

• Kinetic Energy is calculated using the following formula. mv 2 2 • Where: kinetic energy is measured in joules, mass is measured in kilograms (kg), speed is measured in meters per second (m/s) • Formula Ek=1/2 mv 2 or • Therefore we can say that kinetic energy equals work. • Units of kgm 2/s 2 = Nm = J