# Sec 15.2 Objectives 15.2.1 Describe conversions of energy from one form to another. 15.2.2 State and apply the conservation of energy. 15.2.3 Analyze how.

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Sec 15.2 Objectives Describe conversions of energy from one form to another. State and apply the conservation of energy. Analyze how energy is conserved in conversions between kinetic energy and potential energy and solve equations that equate initial energy to final energy. Describe the relationship between energy and mass and calculate how much energy is equivalent to a given mass.

As a meteor traveled through the atmosphere in October 1992, some of its kinetic energy was converted into light and heat. Upon impact, much of the meteor's remaining kinetic energy went into smashing the rear of this car in Peekskill, New York.

Energy Conversion The process of changing energy from one form to another is energy conversion. The striking of a match is a good example. Muscles use chemical energy to move the match. Friction between the match and the matchbox converts kinetic energy into thermal energy. Chemical energy is converted into thermal energy and electromagnetic energy in the flame.

Energy Conversion Can energy be converted from one form into another? Energy can be converted from one form to another – called energy conversion

Energy Conversion Energy is converted from one form to another as this match is lit.

Conservation of Energy
What is the law of conservation of energy? The law of conservation of energy states that energy cannot be created or destroyed.

Conservation of Energy
When energy changes from one form to another, the total energy remains unchanged, even though many energy conversions may occur. In a closed system, the amount of energy present at the beginning of a process is the same as the amount of energy at the end.

Conservation of Energy
The work done by friction changes kinetic energy into thermal energy. In reality, Friction within machinery reduces efficiency. Friction is a major cause of energy consumption in cars and factories. In many cases, most of a falling object’s potential energy is converted into thermal energy because of air resistance (friction).

Conservation of Energy
Although speed skaters slide quickly over smooth ice, they are still slowed down by friction with the air and the surface of the ice.

Energy Conversions What energy conversion takes place as an object falls toward Earth? The gravitational potential energy of an object is converted to the kinetic energy of motion as the object falls.

Energy Conversions One of the most common energy conversions is between potential energy and kinetic energy. An avalanche brings tons of snow from the top of a mountain to the valley floor. The elastic potential energy of a compressed spring is converted into kinetic energy as the spring expands. Energy conversions can go from kinetic to potential energy or from potential to kinetic energy.

Energy Conversions Some gulls use energy conversion to obtain food by dropping oysters onto rocks. Kinetic energy causes the shell to break on collision with the rock.

Energy Conversion in Pendulums
Energy Conversions Energy Conversion in Pendulums A pendulum consists of a weight swinging back and forth from a rope or string. At the highest point in its swing, the pendulum has zero kinetic energy and maximum potential energy. As the pendulum swings downward, potential energy is converted to kinetic energy. At the bottom of the swing, the pendulum has maximum kinetic energy and zero potential energy.

Energy Conversions Pendulum clocks use pendulums to maintain accurate time. The time it takes for a pendulum to swing back and forth once is precisely related to its length.

Energy Conversions Energy Conversion and the Pole Vault In the pole vault, an athlete uses a flexible pole to propel himself over a high bar.

Energy Conversions Some of the pole-vaulter’s kinetic energy is converted into elastic potential energy as the pole bends. The pole springs back into shape, propelling the pole-vaulter upward. As the pole-vaulter rises, his kinetic energy decreases while he gains gravitational potential energy. Once the highest point has been reached, his gravitational potential energy begins to convert back to kinetic energy.

Energy Conversions Energy Conversion Calculations When friction is small enough to be ignored, and no mechanical energy is added to a system, then the system’s mechanical energy does not change. Mechanical energy = KE + PE

Energy Conversions The law of conservation of energy applies to any mechanical process. If friction can be neglected, the total mechanical energy remains constant.

Energy Conversions Conservation of Mechanical Energy At a construction site, a 1.50-kg brick is dropped from rest and hits the ground at a speed of 26.0 m/s. Assuming air resistance can be ignored, calculate the gravitational potential energy of the brick before it was dropped.

Energy Conversions Read and Understand What information are you given?
What unknown are you trying to calculate?

Energy Conversions Plan and Solve What equations or formulas contain the given quantities and the unknown? Because the brick falls without air resistance, the conservation of mechanical energy equation can be used.

Energy Conversions Plan and Solve
You will also need to use the formula for kinetic energy (KE). Note that the KE at the beginning is zero because the brick has not yet begun to fall. Also, when the brick hits the ground, its potential energy is zero. Substitute these values into the conservation of energy formula.

Energy Conversions Plan and Solve Substitute the formula for KE Substitute the known values and calculate the PE.

Energy Conversions Look Back and Check
Is your answer reasonable? Check the answer by finding the initial height of the brick, using PE = 507 J = mgh. Substituting in m and g gives h = 34.5 m. This is a reasonable height for an object in free fall to reach a speed of 26.0 m/s.

Energy Conversions 1. A 10-kg rock is dropped and hits the ground below at a speed of 60 m/s. Calculate the gravitational potential energy of the rock before it was dropped. You can ignore the effects of friction. Answer:

Energy Conversions 1. A 10-kg rock is dropped and hits the ground below at a speed of 60 m/s. Calculate the gravitational potential energy of the rock before it was dropped. You can ignore the effects of friction. Answer: (PE)beginning = (KE)end = ½mv2 =(0.50)(10 kg)(60 m/s)2 = 18,000 J

Energy Conversions 2. A diver with a mass of 70.0 kg stands motionless at the top of a 3.0-m-high diving platform. Calculate his potential energy relative to the water surface while standing on the platform, and his speed when he enters the pool. (Hint: Assume the diver’s initial vertical speed after diving is zero.) Answer:

Energy Conversions 2. A diver with a mass of 70.0 kg stands motionless at the top of a 3.0-m-high diving platform. Calculate his potential energy relative to the water surface while standing on the platform, and his speed when he enters the pool. (Hint: Assume the diver’s initial vertical speed after diving is zero.) Answer:

Energy Conversions 3. A pendulum with a 1.0-kg weight is set in motion from a position 0.04 m above the lowest point on the path of the weight. What is the kinetic energy of the pendulum at the lowest point? (Hint: Assume there is no friction.) Answer:

Energy Conversions 3. A pendulum with a 1.0-kg weight is set in motion from a position 0.04 m above the lowest point on the path of the weight. What is the kinetic energy of the pendulum at the lowest point? (Hint: Assume there is no friction.) Answer: (PE)beginning = mgh = (1.0 kg)(9.8 m/s2)(0.04 m) = 0.4 J; at the beginning, KE = 0, and at the lowest point, PE = 0; therefore (PE)beginning = (KE)end = 0.4 J

Energy and Mass How are energy and mass related? Einstein’s equation, E = mc2, says that energy and mass are equivalent and can be converted into each other.

Energy and Mass Albert Einstein developed his special theory of relativity in This theory included the now-famous equation E = mc2. E is energy, m is mass, and c is the speed of light. The speed of light is an extremely large number, 3.0 × 108 meters per second. A tiny amount of matter can produce an enormous amount of energy.

Energy and Mass Albert Einstein made important contributions to many areas of physics. His theory of special relativity showed that energy and mass are equivalent.

Energy and Mass Suppose 1 gram of matter were entirely converted into energy. E = mc2 = (10–3 kg) × (3 × 108 m/s) × (3 × 108 m/s) = 9 × 1013 kg•m2/s2 = 9 × 1013 J 1 gram of TNT produces only 2931 joules of energy.

Energy and Mass In nuclear fission and fusion reactions, however, large amounts of energy are released by the destruction of very small amounts of matter. The law of conservation of energy has been modified to say that mass and energy together are always conserved.

What energy conversion occurs as a result of friction?
Assessment Questions What energy conversion occurs as a result of friction? chemical energy to thermal energy kinetic energy to potential energy kinetic energy to thermal energy potential energy to thermal energy

What energy conversion occurs as a result of friction?
Assessment Questions What energy conversion occurs as a result of friction? chemical energy to thermal energy kinetic energy to potential energy kinetic energy to thermal energy potential energy to thermal energy ANS: C

Assessment Questions At what point in a pendulum’s swing does it have maximum kinetic energy? the highest point of the swing the lowest point of the swing halfway between the lowest and highest point same at all positions of the swing

Assessment Questions At what point in a pendulum’s swing does it have maximum kinetic energy? the highest point of the swing the lowest point of the swing halfway between the lowest and highest point same at all positions of the swing ANS: C

Assessment Questions Based on Einstein’s equation for the equivalence of energy and mass, how much energy is produced by the conversion of 1 kilogram of mass to energy? 3x103 J 3x105 J 9x105 J 9x1013 J

Assessment Questions Based on Einstein’s equation for the equivalence of energy and mass, how much energy is produced by the conversion of 1 kilogram of mass to energy? 3x103 J 3x105 J 9x105 J 9x1013 J ANS: D

Assessment Questions According to the law of conservation of mass, energy can be converted from one from to another but not created or destroyed. True False

Assessment Questions According to the law of conservation of mass, energy can be converted from one from to another but not created or destroyed. True False ANS: F, law of conservation of energy

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