Download 5.3 Conservation of Energy

5.3
The Law of Conservation of Energy
Energy can neither be created nor destroyed, but only transferred from one form to
another
The total amount of energy before an event occurs must be equal to the total amount of
energy after the event occurs
Example: A ball initially has gravitational potential energy. As the ball falls, the ball loses energy
to the environment due to __________. When the ball hits the ground (an event), the ball loses
energy to the environment (_______and ____________).
time 1
time 2
Total energy before it is dropped at time 1 (eq 1) E T1 = EG1 + Ek1 =
Total energy as the ball hits the pavement at time 2
(eq 2) ET2 = Ek2 + EG2 (EG2 = _______)
We have the expression that
(eq 3) ET1 = ET2 (LAW OF CONSERVATION OF ENERGY)
ELOSS is the ___________________
If the ball (in the above example) initially had 70.0 Joules of energy before it was dropped, and
5 Joules of energy is lost due to ____________ while it is falling, just before the ball hits the
ground the total amount of energy it will have is _________.
Conservation of Mechanical Energy
-
special case of the Law of Conservation of Energy (assumes that energy of an object is not
lost to its environment (no loss of energy to sound, thermal or air resistance as the ball falls)
energy is only transferred from GPE to KE
initial energy is equal to final energy (LAW OF CONSERVATION OF ENERGY)
ET1 = ET2
Ek1 + EG1 = Ek2 + EG2
½mv12 + mgh1 = ½mv22 + mgh2
Example 1: A ball (1.0 kg) is dropped from a height 2.0 meters above the ground. If all of its
gravitational potential energy is transferred to kinetic energy, what is the speed of the ball just
before it hits the floor?
time 1
time 2
Example 2: A ball is initially thrown upwards and has 55 Joules of energy in total (assume energy
is not lost due to ___________). After the ball has traveled 5 m above its original position, the
total amount of energy it has is _______. At maximum height, the total amount of energy the
ball has is ___________. As the ball begins to fall back to the earth, the total amount of
energy the ball has is _________. As you catch the ball (at the original position that it was
thrown at), the total amount of energy the ball has is _________. Describe the energy
conversion that takes place.
Example 3: A roller coaster starts off at a height of 20.0 meters above ground with an initial
speed of 2.0 m/s. What is the final height of the roller coaster when the speed of the coaster
is 7.0 m/s?
Practice Problems:
1) An arrow (why is the mass of the arrow not required???) is fired directly upwards (assume no
energy loss) with a speed of 50.00 m/s (assume it is fired at the reference level (initial height is
0)). Calculate
a) the speed of the arrow when it is 100 m above the reference point
(Ans: 23.24 m/s)
b) the speed of the arrow when it is 125 m above the reference point
(Ans: 7.071 m/s)
c) the maximum height above the reference (v2 is 0 at maximum height)
(Ans: 127.6 m)
2) A rock is tossed off a bridge with an initial speed of 7.2 km/hr (make the bridge height the
reference level (h1 = 0)). Calculate
a) the initial speed of the rock in m/s
b) the speed of the rock after it has fallen 20.0 m
c) the distance the rock has fallen when it reaches a speed of 100.0 km/hr
(Ans: a) 2.0 m/s
b) 19.8 m/s c) 39.16 m)
Example 4: A ball (mass is 5.0 kg) is dropped from a height of 100.0 m. Using the ground as a
reference point, and assuming that mechanical energy is conserved (no energy loss due to air
resistance) complete the following table
Height
(m)
100
80
60
40
20
0
potential
energy Eg
(Joules)
kinetic energy Ek
(Joules)
0
0
Total energy
ET
(Joules)
Speed v (m/s)
0
Example 5: A ball (mass is 2 kg) falls from a height of 500 m.
a) Calculate the speed of the ball just before it hits the ground if energy was not lost due to
air resistance.
b) Calculate the initial amount of energy the ball has.
c) If 20% of the balls original energy is lost while falling due to air resistance, calculate the
energy loss and the speed of the ball just before it hits the ground.
d) If another 10% of the ball’s original energy is lost upon impact, calculate the maximum height
the ball bounces back up to.
Practice Problem:
1) An arrow (mass is 50.0 grams) is fired directly upwards with an initial velocity of 40.0 m/s.
The arrow loses approximately 20.0% of its original kinetic energy. Assume the arrow is
originally at the reference level. Calculate
a) the total amount of energy the arrow started out with
(Ans: 40 Joules)
b) the energy loss
(Ans: -8 Joules)
c) the maximum height the arrow reaches
(Ans: 65.3 m)
d) the total energy the arrow has when it reaches maximum height
(Ans: 32 Joules)