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Conservation of Mechanical Energy

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Learning objectives

I can use the principle of conservation of energy to explain in physics terms how a roller coaster works.

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Success Criteria

  • Calculate the kinetic energy and the potential energy
  • Compute the mechanical energy
  • Prove the law of conservation of energy through mathematical representation

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New Vocabulary

law of conservation of energy

mechanical energy

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Starter

  • List three types of energy

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  • Find the Kinetic energy for 2 kg object moves in 12m/s.

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  • What is the potential energy? give examples.

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  • Find the potential energy for an 6kg-object that locates 18m above the earth surface.

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Review Vocabulary

closed system: a system that does not gain or lose mass

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The Law of Conservation of Energy

  • The law of conservation of energy states that in a closed, isolated system, energy can neither be created nor destroyed; rather, energy is conserved.

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The Law of Conservation of Energy

  • The sum of the kinetic energy and the potential energy of the objects in a system is the system’s mechanical energy (ME).
    • Kinetic energy includes both the translational and rotational kinetic energies.
    • Potential energy includes the gravitational and elastic potential energies.

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Mechanical Energy �of a System

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The Law of Conservation of Energy

  • In some situations, mechanical energy is conserved. In others, some of the mechanical energy is transformed into other forms, such as thermal energy.

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The Law of Conservation of Energy

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Conservation of Mechanical Energy

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The Law of Conservation of Energy

Roller �Coasters

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The Law of Conservation of Energy

Skiing

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The Law of Conservation of Energy

Pendulums

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Starter

  • Find the relationship between kinetic energy and potential energy.

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  • Create a new equation that describe this relationship.

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  • What is the law of conservation of energy

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Practice

Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg

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Practice

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Classwork

A bird is flying with a speed of 18.0 m/s over water when it accidentally drops a 2.00 kg fish. If the altitude of the bird is 5.40 m and friction is disregarded, what is the mechanical energy of the system, and what is the speed of the fish when it hits the water?

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2. A 755 N diver drops from a board 10.0 m above the water’s surface. Find the mechanical energy of the system, and find the diver’s speed 5.00 m above the water’s surface. Then find the diver’s speed just before striking the water.

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3. If the diver in item 2 leaves the board with an initial upward speed of 2.00 m/s, find the diver’s speed when striking the water.

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4. An Olympic runner leaps over a hurdle. If the runner’s initial vertical speed is 2.2 m/s, how much will the runner’s center of mass be raised during the jump? 5. A pendulum bob is released from some initial height such that the speed of the bob at the bottom of the swing is 1.9 m/s. What is the initial height of the bob?

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Classwork A.k

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Classwork A.k

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Starter

https://www.youtube.com/watch?v=xXXF2C-vrQE

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EVALUATE THE ANSWER

  • The answer is reasonable for a diver entering the water.

Use with Example Problem 5.

Problem

A 68.2-kg diver steps off a 5.0-m diving platform. Ignoring air resistance, what is the kinetic energy and velocity of the diver as she enters the water?

Response

SKETCH AND ANALYZE THE PROBLEM

  • Sketch the situation. Indicate the reference level for GPE.
  • List the knowns and unknowns.

KNOWN

UNKNOWN

hi = 5.0 m

hf = 0 m

Kef = ?

m = 68.2 kg

vi = 0 m/s

vf = ?

SOLVE FOR THE �UNKNOWN

  • The final GPE and �the initial KE are 0 J. �Determine the initial GPE.

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  • Use conservation of energy to determine the final KE.

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  • Determine the final velocity.

+x

h = 0 m

h = 5.0 m

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Quiz

a closed, connected system

D

a closed, isolated system

C

an open, connected system

B

an open, isolated system

A

The law of conservation of energy is defined for what type of system?

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CORRECT

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Quiz

energy transformation

D

mechanical energy

B

energy conservation

C

thermal energy

A

What is the sum of the kinetic and the potential energy of the objects in a system called?

2.

CORRECT

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Quiz

PE and KE stay the same.

D

PE decreases, and KE increases.

B

PE decreases, and KE decreases.

C

PE increases, and KE increases.

A

As a skier goes down a slope, what happens to her kinetic energy (KE) and potential energy (PE)?

3.

CORRECT