Download Chapter 15.2 math practice

Name
Chapter 15
Class
Date
Energy
Section 15.2 Energy Conversion and
Conservation
(pages 453–461)
Using the Law of Conservation of Energy
Content and Vocabulary Support
Energy Conversion and Conservation
Energy can be changed from one form to another. The process of
changing energy from one form to another is called energy
conversion. For example, a light bulb changes electrical energy into
thermal energy (heat) and electromagnetic energy (light). The law of
conservation of energy states that energy cannot be created or
destroyed. Thus, when energy changes from one form to another, the
amount of energy remains the same.
Conservation of Mechanical Energy
Recall that mechanical energy is the total kinetic and potential energy
of an object.
Mechanical energy ⫽ KE ⫹ PE
Because of the law of conservation of energy, total mechanical energy
remains constant. This can be written as:
(KE ⫹ PE)beginning ⫽ (KE ⫹ PE)end
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Physical Science Math Skills and Problem Solving Workbook
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Examples of Energy Conversion
One of the most common energy conversions is between potential
energy and kinetic energy. Whenever an object falls, the gravitational
potential energy of the object is converted to the kinetic energy of
motion. When a spring is released, it also results in the conversion of
potential energy to kinetic energy.
The swinging of a pendulum and the movement of a pole vaulter
are other examples of kinetic and potential energy conversions. When
a pendulum swings from side to side, it has kinetic energy. At the
high point of each swing, the pendulum momentarily stops. At that
point it has gravitational potential energy but no kinetic energy. Then
it swings in the opposite direction, and its potential energy is
converted to kinetic energy again. A pole vaulter runs and uses her
pole to gain kinetic energy that helps propel her into the air. In the air,
she has gravitational potential energy. As she falls back to the ground,
her potential energy is converted back to kinetic energy.
Name
Class
Date
Section 15.2 Energy Conversion and Conservation
Solved Examples
Example 1:
A 1.25-kilogram stone fell from a cliff and struck the
ground at a speed of 29.4 meters per second. What was
the gravitational potential energy of the stone before it
fell?
Given: m ⫽ 1.25 kg v ⫽ 29.4 m/s
Unknown: PEbeginning
KEbeginning
PEend
KEend
Equations: KE ⫽ 21 mv2 and (KE ⫹ PE)beginning ⫽ (KE ⫹ PE)end
Solution: The stone has no kinetic energy until it starts
to fall, so KEbeginning equals zero. After the
stone lands on the ground, it no longer has
potential energy, so PEend equals zero.
Calculate KEend using the first equation and
given values:
KEend ⫽ 12 ⫻ 1.25 kg ⫻ (29.4 m/s)2 ⫽ 540 J
Substitute the known values into the second
equation, and solve for PEbeginning:
0 ⫹ PEbeginning ⫽ 540 J ⫹ 0; PEbeginning ⫽ 540 J
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Example 2:
A 56-kilogram teen attached to a bungee cord jumps off
a 10-meter-high tower. What is her kinetic energy when
she reaches the bottom of her fall?
Given: m ⫽ 56 kg
h ⫽ 10 m
Unknown: KEend
PEbeginning
KEbeginning
PEend
Equations: PE ⫽ mgh and (KE ⫹ PE)beginning ⫽ (KE ⫹ PE)end
Solution: By the same reasoning as in Example 1,
KEbeginning and PEend equal zero. Calculate
PEbeginning using the first equation and given
values:
PEbeginning ⫽ 56 kg ⫻ 9.8 m/s2 ⫻ 10 m ⫽ 5,488 J
Substitute the known values into the second
equation, and solve for KEend:
0 ⫹ 5,488 J ⫽ KEend ⫹ 0; KEend ⫽ 5,488 J
Physical Science Math Skills and Problem Solving Workbook
67
Name
Class
Date
Practice Exercises
A book with 67 joules of gravitational potential energy
fell from a shelf and landed on the floor. What was its
kinetic energy when it landed on the floor?
Exercise 2:
A 0.2-kilogram object is lifted into the air and then
dropped to the floor. If it is moving at a speed of
3 meters per second when it hits the floor, what was its
gravitational potential energy before it was dropped?
Exercise 3:
Lance threw a ball straight up into the air. The ball’s
gravitational potential energy at its peak height was
0.4 joules, and its speed when it hit the ground was
4 meters per second. What was the mass of the ball?
Exercise 4:
Alfredo, who has a mass of 60 kilograms, jumped off a
retaining wall. His kinetic energy when he landed on
the ground was 882 joules. How high was the wall?
Exercise 5:
A water feature in a garden recycles water with a
pump. Water is pumped from a stone basin up through
a pipe 1 meter high. At that height, the water flows out
through a tap and falls down through the air to the
basin below, where the cycle begins again. What is the
gravitational potential energy of 2.5 kilograms of water
at the top of the pipe? How fast is the falling water
moving by the time it reaches the basin?
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Physical Science Math Skills and Problem Solving Workbook
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Exercise 1: