5.2 energy definition of kinetic energy kinetic energy is the energy of motion kinetic energy...

5.2 Energy

DEFINITION OF KINETIC ENERGY

Kinetic energy is the energy of motion

Kinetic energy depends on an objects speed and mass.

DEFINITION OF KINETIC ENERGY

The kinetic energy KE of and object with mass m and speed v is given by

221KE mv

5.2 Energy

Scalar quantitySI Unit for Kinetic Energy is the Joule

Kinetic Energy

• What are the SI units for KE?– kg•m2/s2 or N•m or J

Work and Kinetic Energy

• KE is the work an object can do if the speed changes.

• Wnet is positive if the speed increases.

Question #8

Calculate the kinetic energy of an 8.0X104kg airliner flying at 600.0 km/h.

1.1X109 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 #11A 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 Energy

DEFINITION OF POTENTIAL ENERGY

~Stored Energy~Gravitational potential energy depends on the

height from a zero level

mghPE

fi hhmg PE

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.

mghPE

fi hhmg PE



mghPEg

fi hhmgPE gravity

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•m2/s2 or N•m or J

• The height (h) depends on the “zero level” chosen where PEg = 0.


Example A Gymnast on a Trampoline

The gymnast leaves the trampoline at an initial height of 1.20 mand reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the gymnast?


2212

f21W imvmv

mghW gravity

221

ifi mvhhmg

foo hhgv 2

sm40.8m 80.4m 20.1sm80.92 2 ov

5.2 Elastic Potential Energy

DEFINITION OF ELASTIC POTENTIAL ENERGY

The energy stored in a spring that is compressed or stretched

2 elastic

2

1PE kx

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


DEFINITION OF ELASTIC POTENTIAL ENERGY

Increasing the spring constant indicates a stiffer spring

K = Spring Constant

SI unit = N · m

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


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


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


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

KEPEME

DEFINITION OF MECHANICAL ENERGY

The mechanical energy is the sum of potential energy and kinetic energy.

Mechanical Energy (ME)

• ME = KE + PEg + PEelastic

– 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

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


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


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


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 103 J


Question #20

What is the kinetic energy of a 1250kg car moving at 45.0 km/h?

9.77 X 104 J


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


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 at the instant the book is

released.• 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 just as the book reaches the floor.

• Answer: PE = 0 J, KE = 19.6 J

5.2 energy definition of kinetic energy kinetic energy is the energy of motion kinetic energy...

Documents