Transcript Work2 - I Pride Students
5.2 Energy
DEFINITION OF KINETIC ENERGY Kinetic energy is the energy of motion Kinetic energy depends on an objects speed and mass.
5.2 Energy
DEFINITION OF KINETIC ENERGY The kinetic energy KE of and object with mass
m
and speed
v
is given by KE 1 2
mv
2 Scalar quantity SI Unit for Kinetic Energy is the Joule
Kinetic Energy
• What are the SI units for KE?
– kg•m 2 /s 2 or N•m or J
Work and Kinetic Energy
• •
KE
is the work an object can do if the speed changes.
W net
is positive if the speed increases.
5.2 Energy
Question #8
Calculate the kinetic energy of an 8.0X10
4 kg airliner flying at 600.0 km/h.
1.1X10
9 J
5.2 Energy
Question #9
Two bullets have masses of 3.0g and 6.0g, respectively. Both are fired with a speed of 40.0 m/s. Which bullet has more kinetic energy? What is the ratio of their kinetic energies?
– The bullet with the greater mass – 2 to 1
5.2 Energy
Question #10
Two 3.0g bullets are fired with velocities of 40.0 m/s and 80.0m/s respectively. What are their kinetic energies? Which bullet has more kinetic energy? What is the ratio of their kinetic energies?
– 2.4 J – The bullet with the more speed – 4 to 1
5.2 Energy
Question #11
A running student has half the kinetic energy that his younger brother has. The student speeds up by 1.3 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 students and his brother?
– 3.2 m/s – 6.4 m/s
5.2 Gravitational Potential Energy
DEFINITION OF POTENTIAL ENERGY ~Stored Energy ~Gravitational potential energy depends on the height from a zero level PE
mgh
PE
mg
h i
h f
5.2 Gravitational Potential Energy
DEFINITION OF POTENTIAL ENERGY The potential energy (PE) is defined by the mass and height of the object above an arbitrary zero level.
PE
mgh
PE
mg
h i
h f
5.2 Gravitational Potential Energy
PE g
mgh PE
gravity
mg
h i
h f
Potential Energy
• Energy associated with an object’s potential to move due to an interaction with its environment – A book held above the desk – An arrow ready to be released from the bow • Some types of PE are listed below.
– Gravitational – Elastic – Electromagnetic
Gravitational Potential Energy
• What are the SI units?
– kg•m 2 /s 2 or N•m or J • The height (
h
) depends on the “zero level” chosen where
PE g
= 0.
5.2 Gravitational Potential Energy
Example A Gymnast on a Trampoline
The gymnast leaves the trampoline at an initial height of 1.20 m and reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the gymnast?
5.2 Gravitational Potential Energy
W 1 2
mv
f 2 1 2
mv i
2
W
gravity
mgh mg
h i
h f
1 2
mv i
2
v o
2
g
h o
h f
v o
2 9 .
80 m s 2 1 .
20 m 4 .
80 m 8 .
40 m s
5.2 Elastic Potential Energy
DEFINITION OF ELASTIC POTENTIAL ENERGY The energy stored in a spring that is compressed or stretched PE elastic 1 2
kx
2
K = Spring Constant X= Distance the spring is compressed or stretched
Elastic Potential Energy
• The energy available for use in deformed elastic objects – Rubber bands, springs in trampolines, pole-vault poles, muscles • For springs, the distance compressed or stretched =
x
5.2 Elastic Potential Energy
DEFINITION OF ELASTIC POTENTIAL ENERGY Increasing the spring constant indicates a stiffer spring
K = Spring Constant SI unit = N · m
5.2 Elastic Potential Energy
Question #12
Staples inside a stapler are kept in place by a spring with a relaxed length of 0.115m. If the spring constant is 51.0 N/m, how much elastic potential energy is stored in the spring when its length is 0.150 m?
3.1 X 10 -2 J
5.2 Elastic Potential Energy
Question #13
A spring with a force constant of 5.2 N/m has a relaxed length of 2.45m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57m. Calculate the elastic potential energy stored in the spring. 3.3 J
5.2 Elastic Potential Energy
Question #14
A 40.0kg child is in a swing that is attached to ropes 2.00m long. Find the gravitational potential energy associated with the child relative to the child’s lowest position under the following conditions: When the ropes are horizontal.
785 J
5.2 Elastic Potential Energy
Question #15
A 40.0kg child is in a swing that is attached to ropes 2.00m long. Find the gravitational potential energy associated with the child relative to the child’s lowest position under the following conditions: When the ropes make a 30.0
° angle with the vertical.
105 J
5.2 Mechanical Energy
DEFINITION OF MECHANICAL ENERGY The mechanical energy is the sum of potential energy and kinetic energy.
ME
PE
KE
Mechanical Energy (
ME
)
• •
ME
=
KE
+
PE g
+
PE elastic
– Does not include the many other types of energy, such as thermal energy, chemical potential energy, and others
ME
is not a new form of energy.
– Just a combination of
KE
and
PE
5.2 Mechanical Energy
Question #16
What forms of energy are involved in the following situations: • A bicycle coasting along a level road – Kinetic • Throwing a football – Kinetic and gravitational potential • Winding a hairspring of a clock – Elastic potential
5.2 Mechanical Energy
Question #17
A pinball bangs against a bumper, giving the ball a speed of 42 cm/s. If the ball has a mass of 50.0g, what is the ball’s kinetic energy in joules?
4.4 X 10 -3 J
5.2 Mechanical Energy
Question #18
A spoon is raised 21.0 cm above a table. If the spoon and its contents have a mass of 30.0g, what is the gravitational potential energy associated with the spoon at the height relative to the surface of the table?
6.18 X 10 -2 J
5.2 Mechanical Energy
Question #19
A 65kg diver is poised at the edge of a 10.0m high platform. Calculate the gravitational potential energy associated with the position of the diver. Assume the zero level is at the surface of the pool?
6.4 X 10 3 J
5.2 Mechanical Energy
Question #20
What is the kinetic energy of a 1250kg car moving at 45.0 km/h?
9.77 X 10 4 J
5.2 Mechanical Energy
Question #21
The force constant of a spring in a child’s toy car 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?
4.0 X 10 -2 J
5.2 Mechanical Energy
Question #22
A 25.0 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 ?
7.96 m
Classroom Practice Problems
• Suppose a 1.00 kg book is dropped from a height of 2.00 m. Assume no air resistance.
– Calculate the
PE
and the
KE
book is released.
at the instant the • Answer:
PE
= 19.6 J,
KE
= 0 J – Calculate the
KE
and
PE
when the book has fallen 1.0 m. (Hint: you will need an equation from Chapter 2.) • Answer:
PE
= 9.81 J,
KE
= 9.81 J – Calculate the
PE
and the
KE
reaches the floor.
just as the book • Answer:
PE
= 0 J,
KE
= 19.6 J