Resource Lesson
Mechanical Energy
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Energy
is defined as the ability to do work and is a scalar quantity. Energy has no direction, only magnitude. Mechanical energy comes in two varieties:
kinetic energy
(KE) and
potential energy
(PE).
Kinetic Energy
Kinetic energy represents the energy caused by an object's motion
KE = ½mv
^{2}
where
v
is the object's actual speed, that is, the magnitude of the object's instantaneous resultant velocity. In this formula,
m
must be measured in kg and
v
must be measured in m/sec. Note that this collection of units
kg (m/sec)
^{2}
= kg m
^{2}
/sec
^{2}
is called a
joule
(J).
Refer to the following information for the next three questions.
Suppose the skater shown below has a mass of 25 kg and is moving at a speed of 8 m/sec along a level surface.
1. How much KE would he possess?
2. How would his kinetic energy change if his speed doubled?
3. How would the kinetic energy of a second skater having twice as much mass but still moving at 8 m/sec compare with the kinetic energy of our original skater?
Notice that the kinetic energy of an object is a scalar quantity whose value is directly proportional to the object's mass and is also directly proportional to the square of the object's velocity.
Refer to the following information for the next question.
4. How do the kinetic energies of these two carts compare?
Refer to the following information for the next question.
The following three 1-kg projectiles are all released at the same speed, 20 m/sec. However, the first one is released vertically, the second one is released at 37º, and the third one is released horizontally.
5. How do the initial kinetic energies of these three projectiles compare?
Gravitational Potential Energy
This type of potential energy represents the energy an object possesses by virtue of its location in a gravitational field.
PE = mgh
where
h
is the height above an arbitrary zero level that is convenient for the solution of the problem. For instance, the zero level might be assigned as the base of a cliff for a projectile being thrown from the top of the cliff or the zero level might be the floor for a marble rolling off a table onto the ground.
In this formula,
m
must be measured in kg,
g
equals 9.8 m/sec
^{2}
, and
h
is in meters. Note that this collection of units
kg (m/sec
^{2}
)(m) = kg (m
^{2}
/sec
^{2}
) is also a
joule
(J).
The expression
mg
represents the objects weight or the force of gravitational attraction between the earth and the object. Forces are measured in newtons. Thus the expression
Nm also equals a
joule
(J).
Refer to the following information for the next two questions.
The table is 1-meter tall and the apple has a mass of 100 grams.
What is the potential energy of the apple with respect to the top of the table?
What is the potential energy of the apple with respect to the floor at the base of the table?
Notice that the potential energy of an object is a scalar quantity whose value is directly proportional to the object's mass and is also directly proportional to the object's height above an arbitrarily chosen zero level.
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