Download Energy Conservation ANSWERS

MONDAY, FEB 7, 2005
Hand in Work/Machine Labs
Take out compound machine HW and hand in.
--------------------Today,
Go over Energy Project Assignment
MECH ENERGY Done by Feb 16?
Introduction to Mechanical Energy Changes.
Example of Mechanical Energy Changes:
I take a spring loaded dart gun and fire it into the air. I push on the 0.1 Kg dart with 3
Newtons of force.
What type of energy does it have at each point in its journey?
ENERGY CHANGES ….. IF no friction/heat
Δ ME = Δ ME
Start
GPE
mgh
Finish
+
+
KE
+ EPE
2
1/2mv + 1/2kx2
=
=
GPE
mgh
+
+
KE
+ EPE
2
1/2mv + 1/2kx2
KINETIC AND POTENTIAL ENERGY CHANGES
Label the points at which:
______The skier is gaining speed
______ The point at which the skier is moving the fastest
________ The point at which the skier has the greatest amount of potential energy
_____ The point at which the potential energy is changing to kinetic energy
_____ The point at which the skier has the greatest amount of kinetic energy
____ The point at which kinetic energy is changing to potential energy
Explain why the skier will never return to the height of point A.
Where and how is mechanical energy “lost?”
A tennis ball undergoes several energy changes as it travels towards a player, is struck,
and rapidly speeds back over the net. Describe these energy changes using the concepts
of kinetic and potential energy
CONSERVATION OF ENERGY DIAGRAM SKILLS
A roller coaster with a mass of m moves along a smooth track as diagrammed in the
graph. The car leaves point A with no initial velocity and travels to other points along the
track. The zero energy level is taken as the energy of point A.
1a) What is the car’s kinetic energy at point A?
b) What is the potential energy associated with the car at point A?
c) What is the car’s kinetic energy at point B?
d) What is the cat’s potential energy at point B?
2a) What is the speed of the car at point A?
b) What is the speed of the car at point B?
3. Assume the mass of the car is 65 kg, and it starts at 30 m above the ground (each
square is 5 m). Use the graph above to find the kinetic energy, potential energy, and
velocity for points C,D,E<F,G
Location
A
B
C
D
E
F
G
KEA
PEA
KE location
PE location
V location
4. For each location, what do you notice about the sum of the kinetic and potential
energies?
KINETIC AND POTENTIAL ENERGY:
Section 5-2
Pg. 173
#2
Two bullets have the mass of 3 g and 6 g, respectively. Both are fired with a
speed of 40 m/s. Which bullet has more kinetic energy? What is the ratio of their kinetic
energies?
#3
Two 3 g bullets are fired with velocities of 40 m/s and 80 m/s respectively. What
are their kinetic energies? Which bullet has more kinetic energy? What is the ratio of
their kinetic energies?
Section 5-2 pg 177
#3
A spring with a force constant of 5.2 N/m has a relaxed length of 2.45 m. When a
mass is attached to the end of the spring and allowed to come to rest, the vertical length
of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring.
#4
A 40 kg child is in a swing that is attached to ropes 2 m long. Find the
gravitational potential energy associated with the child relative to the child’s lowest
position under the following conditions:
a) when the ropes are horizontal
b) when the ropes make a 30 degree angle with the vertical. (half off the ground)
c) at the bottom of the circular arc.
*** Honors
Section 5-2 pg. 173 # 4
A running student has half the kinetic energy that his brother has. The student
speeds up by 1 m/s, at which point he has the same kinetic energy as his brother. If the
student’s mass is twice as large as his brother’s mass, what were the original speeds of
both the student and his brother?
**Honors:
Using Motion Equation # 5, prove that starting gravitational potential energy and
ending kinetic energy are equal for a falling object.
Using Motion Equation # 5, Newton’s Laws and the definition of work, prove that
starting elastic potential energy and ending kinetic energy are equal for an object pulled
back on a spring.
Section Review 5-2 pg. 178
1. What forms of energy are involved in the following situations?
a) a bicycle coasting along a level track.
b) heating water
c) throwing a football
d) winding the hairspring of a clock.
2. How do the forms of energy in item 1 differ from another? Be sure to discuss
mechanical vs. non-mechanical, kinetic vs. potential, and gravitational vs. elastic.
3. A pinball bangs against a bumper, giving the ball a speed of 42 cm/s. If the ball has a
mass of 50 g, what is the ball’s kinetic energy in joules?
4. A spoon is raised 21 cm above a table. If the spoon and its contents have a mass of 30
g, what is the gravitational potential energy associated with the spoon at that height
relative to the table?
5. A 65 kg diver is poised at the edge of a 10 m high platform. Calculate the gravitational
potential energy associated with the position of the diver. Assume the zero level is the
surface of the pool.
6. What is the kinetic energy of a 1250 kg car moving at 45 km/hr?
7. The force constant of a spring is 550 N/m. How much elastic potential energy is stored
in the spring if the spring is compressed a distance of 1.2 cm? What is the force being
used to compress the spring?
8. a 25 kg falling object strikes the ground with a speed of 12.5 m/s. IF the kinetic energy
of the object when it hits the ground is equal to the gravitational potential energy at some
height above the ground, what is the height?