Conservation of Energy

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Learn about open and closed system and how to solve for problems using the conservation of energy formula with mechanical energy

Conservation of Energy Variables

Name	Variable	Unit	Unit Abbreviation
Mechanical Energy	ME	Joule	J
Potential Energy	PE	Joule	J
Kinetic Energy	KE	Joule	J
Mass	m	Kilogram	kg
Acceleration Due To Gravity	g	Meters per second squared	m/s²
Velocity	v	Meters per Second	m/s
Height or distance	h or d	Meters	m
Weight	F_w	Newtons	N

Systems and Environment

A system is an object or collection of objects defined as those being studied.

An example of a system could be a roller coaster. A smaller example may be the roller coaster cart itself
Objects outside a system are considered external and in its environment or surroundings.

If your system was just the roller coaster cart would lose heat resulting from friction with the track. The track would be considered outside the system and in the roller coasters surroundings

Two types of systems are open and closed systems

A closed system does not interact with the environment and has no outside forces or energy transfer.

An open system does interact with the environment and has external forces or energy transfer.

The Law of Conservation of Energy

Energy is neither created nor destroyed just transformed from one form to another.

In closed or isolated systems, energy would remain constant in the system
Open systems would have energy lost to the environment, but not lost to the universe

Different Forms of Energy

Chemical Potential Energy
Mechanical (ME): Kinetic Energy (KE) & Potential Energy (PE)
Light
Heat
Nuclear
Electric

When a firecracker explodes, chemical potential energy converts into light, heat, and kinetic energy.

Energy is not lost, just converted

Energy is conserved in the universe, not an open system

A roller coaster cart would lose energy to the environment
As potential energy converts to kinetic energy, some energy is lost as heat

Mechanical energy is energy in motion (kinetic energy) or energy that can become motion (potential energy).

Total mechanical energy is the kinetic energy plus potential energy.
Our focus will be on mechanical energy and conversion of one form (potential energy) to another form (kinetic energy) in this lesson

Conservation of Energy Equation

The following equations will require substitutions determined by the question itself. These substitutions will involve PE = mgh and KE = 1/2 mv² from our mechanical energy lesson found here.

Watch our video at the top of this page and walk through how to do this with us as we visit the following problems.

Mass can cancel our of the conservation of energy equation in its expanded form when each part has the mass variable.

Ideal (Perfect, No Energy Lost) Situations

Potential energy gets transformed to kinetic as an object falls
The overall mechanical energy did not change

Example Conservation of Energy Problems

Q1: A 1.5kg rock has 50 J of potential energy when dropped. What is its kinetic energy when it hits the ground?

Q2: A 1.5kg rock is dropped from a height of 10 meters. What is its kinetic energy when it hits the ground?

Q3: A 1.5kg rock is dropped from a height of 10 meters. What is its velocity when it hits the ground?

Q4: A 1.5kg rock falling at 6 m/s is 35 m off the ground. What is its velocity when it hits the ground?

Q5: A 1.5kg rock falling at 6 m/s is 35 m off the ground. What is its velocity 5 meters off the ground?

Q6: A 1.5kg rock falling at 6 m/s is 35 m off the ground. How much kinetic energy does it have at the moment it hits the ground?

Q7: How much potential energy does a 1.5kg rock have when dropped if it is going 26 m/s when 5 meters from the ground?

Q8: How much mechanical energy does a 1.5kg rock have when dropped if it is going 26 m/s when 5 meters from the ground?

Q9: How much mechanical energy does a 1.5kg rock have when dropped has 20 J of kinetic energy and 15 J of potential energy a few seconds later?

Use this equation if a problem asks for how much heat is lost:

ME_i = ME_f + Heat

Heat would leave an open system

Q10: If a 1.5kg rock when dropped had 45J of potential energy when dropped and 43J of kinetic energy when it hit the ground, how much converted to heat?

Conservation of Energy Problem Set

Clicking on check answer will give you the answer watch the end of the video at the top of the page to see the work to get the solution.

When you drop an object does the following increase, decrease, or stay the same in an ideal situation as it falls to the ground?

1A) Kinetic Energy

Increases

1B) Potential Energy

Decreases

1C) Mechanical Energy

Remains Unchanged (In an ideal situation with no heat lost)

1D) If the situation was not ideal, what most likely would the energy be lost as?

Heat

2. How much kinetic energy does a 1.2 kg ball have the moment it hits the ground 3.5 meters below when it starts from rest?

42 J

3. How fast is a 1.2 kg ball traveling the moment it hits the ground 3.5 meters below when it starts from rest?

8.37 m/s

4. A 3.5 kg ball falls from a height of 12 meters. How fast is it traveling when still 5 meters off the ground?

11.83 m/s

5. A 3.5 kg ball falls from a height of 12 meters. How much kinetic energy does it have when still 5 meters off the ground?

245 J

6. An roller coaster cart is traveling 4 m/s at the top of a hill 61 meters off the ground. How fast is it traveling at top of a second hill 24 meters off the ground?

27.49 m/s

7. A 0.16 kg pool ball is shot off a 0.73 m high table and the ball hits the floor with a speed of 7.1 m/s. How fast was the ball moving when it left the pool table?

5.98 m/s

8A) A 0.16 kg pool ball was traveling at 12 m/s while 0.78 meters off the ground. How much mechanical energy does it have when it hits the ground?

12.77 J

8B) How much did it start with?

12.77 J

If no heat or other forms of energy lost the initial mechanical energy equals the final mechanical energy