10.3 Energy and Conservation of Energy

Chapter 10 Objectives  Calculate the mechanical advantage for a lever or rope and pulleys.  Calculate the work done in joules for situations involving force and distance.  Give examples of energy and transformation of energy from one form to another.  Calculate potential and kinetic energy.  Apply the law of energy conservation to systems involving potential and kinetic energy.

Chapter Vocabulary  chemical energy  closed system  law of conservation  of energy  electrical energy  fulcrum  gears  input  input arm  input force  joule  kinetic energy  lever  machine  mechanical  advantage  mechanical energy  mechanical system  nuclear energy  output  output arm  output force  potential energy  pressure energy  radiant energy  ramp  rope and pulley  screw  simple machine  thermal energy  work

Inv 10.3 Energy and Conservation of Energy Investigation Key Question: How is motion on a track related to energy?

10.3 Energy and Conservation of Energy  Energy describes a system’s ability to cause change.  A system that has energy has the ability to do work.  Energy is measured in the same units as work because energy is transferred during the action of work.

10.3 Different forms of energy  Mechanical energy is the energy possessed by an object due to its motion or its position.  Radiant energy includes light, microwaves, radio waves, x-rays, and other forms of electromagnetic waves.  Nuclear energy is released when heavy atoms in matter are split up or light atoms are put together.  The electrical energy we use is derived from other sources of energy.

The workings of the universe can be viewed as energy flowing from one place to another and changing back and forth from one form to another.

10.3 Potential Energy  Objects that have potential energy do not use the energy until they move.  An object’s potential energy comes from the gravity of Earth.  Technically, energy from height is called gravitational potential energy.  Other forms of potential energy also exist, such as potential energy stored in springs.

10.3 Potential Energy E p = mgh Height (m) Mass (kg) Potential Energy (joules) Acceleration of gravity (m/sec 2 )

 You are asked for potential energy and time.  You are given mass, height and work done per second.  Use: E p = mgh.  Solve for E p = (102 kg) (9.8 N/kg) (4 m) = 3,998 J.  At a rate fof 50 J/s, it takes 80 s to push the cart up the ramp. Calculating potential energy A cart with a mass of 102 kg is pushed up a ramp. The top of the ramp is 4 meters higher than the bottom. How much potential energy is gained by the cart? If an average student can do 50 joules of work each second, how much time does it take to get up the ramp?

10.3 Kinetic Energy  Energy of motion is called kinetic energy.  The kinetic energy of a moving object depends on two things: mass and speed.  Kinetic energy is proportional to mass.

10.3 Kinetic Energy  Mathematically, kinetic energy increases as the square of speed.  If the speed of an object doubles, its kinetic energy increases four times (mass is constant).

10.3 Kinetic Energy E k = 1 mv 2 2 Speed (m/sec) Mass (kg) Kinetic Energy (joules)

10.3 Kinetic Energy  Kinetic energy becomes important in calculating braking distance.

10.3 The formula for kinetic energy  A force (F) is applied to mass (m) and creates acceleration (a).  After a distance (d), the ball has reached speed (v), therefore the work done is its mass times acceleration time distance:  W= fd = (ma) x d = mad  Also: d = ½ at 2  Replace d in the equation for work, combine similar terms:  W= ma (½ at 2 ) = ½ ma 2 t 2  Also: v = at, so v 2 = a 2 t 2  Replace a 2 t 2 by v 2 shows that the resulting work is the formula for kinetic energy:  W = ½ mv 2

 You are asked for kinetic energy and stopping distance  You are given mass, speed and force of brakes.  Use E k = 1 / 2 mv 2 and W= fd  Solve for E k = ½ (1,300 kg) ( 30 m/s) 2 = 585,000 J  To stop the car, work done by brakes = E k of car, so W = E k  Solve for distance = W ÷ f = 585,000J ÷ 9,500 N = 62 m Calculating kinetic energy A car with a mass of 1,300 kg is going straight ahead at a speed of 30 m/s (67 mph). The brakes can supply a force of 9,500 N. Calculate: a) The kinetic energy of the car. b) The distance it takes to stop.

10.3 Law of Conservation of Energy  As energy takes different forms and changes things by doing work, nature keeps perfect track of the total.  No new energy is created and no existing energy is destroyed.

10.3 Energy in a closed system  The conservation of energy is most useful when it is applied to a closed system.  Because of the conservation of energy, the total amount of matter and energy in your system stays the same forever.

10.3 Energy in a closed system  The total energy in the system is the potential energy of the ball at the start.  Later, the ball is at a lower height (h) moving with speed (v) and has both potential and kinetic energy.

 Every day in the United States the average person uses about 90 million joules of electrical energy.  This energy comes from many sources, including burning coal, gas and oil, nuclear power, and hydroelectric power. Hydroelectric Power  In hydroelectric power, the potential energy of falling water is converted to electricity.  No air pollution is produced, nor hazardous wastes created.