# Momentum and Energy – Energy and its Conservation

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Lab 4.1 – Momentum and Energy – Energy and its Conservation

Objective To find out about the different forms of energy and the principle of conservation of energy.

Materials Computer. Phet Simulation

More to read: Essay on Energy Utilization

Introduction This lab introduces the concept of energy and the principle of the conservation of energy. Before discussing either energy or its conservation, it is important to specify the object or set of object for which we are finding the energy. This object or set of interacting objects is called the system. All other objects in the universe that are not a part of the system are said to be the environment.

In simple terms, conservation of energy for a system states that the sum of the total initial energy and the energy transferred between the system and the environment equals the total final energy of the system:

Etotal initial + Energy Transfer = Etotal final

Energy can be stored in a system via different storage mechanisms. In this lab we will consider only two storage mechanisms, kinetic energy (KE) and gravitational potential energy (PEg). The definitions for these energy types are shown in the table below.

Energy Symbol Meaning Definition Meaning of Variables in Definition

Kinetic Energy KE Energy of motion 1 /2mv 2 m = mass of object v = speed of object

Gravitational

Potential

Energy

PEg

Energy stored

in object/earth

system

mgh

m = mass of object

h = height relative to zero height

The location of h=0 is arbitrary.

In the expression for gravitational potential energy, (mgh), note that g is equal to positive 9.8m/s2. g does not equal a negative number!

The total energy of a system is the sum of the kinetic and gravitational potential energies:

Etotal = KE + PEg —————————(equation 1)

Question 1

Complete the following table by using the definitions above to determine when each quantity is positive, zero or negative. Two of the answers have been filled in for you as examples.

Quantity Sign of

Quantity Meaning

Kinetic

Energy

Positive

Zero Object is at rest

Negative

Gravitational

Potential

Energy

Positive Object is located above h=0.

Zero

Negative

There are various ways to transfer energy between the system and the environment. Work (W) is one of these ways. In this lab, we will only discuss work for an object moving along a straight line that is exerted by a force that is directed along that line. For this particular case work, W is defined as W = ± Fext d

Where Fext is an external force acting on an object and d is the distance it travels under the influence of that external force.

If the object moves in the same direction as Fext, then the work is positive.

If the object moves in the direction opposite to the direction of Fext, then the work is negative.

The SI Units of energy and of work are Joules

Conservation of energy states:

KEi + PEgi + W = KEf + PEgf

(Etotal)i + W = (Etotal)f —————–(equation 2)

Here i and f indicate initial and final states of the system. In this expression, the work is done by agents outside of the system on an object inside of the system.

We say that the energy of a system is conserved whenever (Etotal)i = (Etotal)f.

Question 2

What must the work be for (Etotal)i to be equal to (Etotal)f?

Experiment 1: Consider the situation shown at right that involves a girl skateboarding on a frictionless track as shown. The girl rides down the hill, reaches the bottom, rises on the other side of the track, turns around, then rides down the hill once again. Assume the system consists of the girl, her skateboard, and the earth. The track is a part of the environment, not a part of the

system.

Predict the following. For the potential energy you can consider h=0 to be at the bottom of the track.

Prediction 1 While the girl is riding down the hill:

a) Is the kinetic energy positive, or zero? (Hint: take a look at your answer to question 1.)

b) Is the height of the girl positive, negative or zero? (Hint: consider height h=0 at the bottom of the track.)

c) Is the gravitational potential energy positive, negative or zero? (Hint: take a look at your answer to question 1.)

d) Is the total energy positive, negative or zero? (Hint: look at the definition of total energy in equation 1.)

e) Does an external force act on the girl? If so what/who is exerting the force and in what direction?

f) Is the work performed on the girl by this external force positive, negative or zero? (Hint: does the girl move in the same direction as the external force, in he opposite direction, or perpendicular to it?)

g) Is the girl speeding up, slowing down, or moving at constant speed?

h) Is the kinetic energy increasing, decreasing, or remaining constant? (Hint: take a look at the definition of kinetic energy in the table on page 1.)

i) Is the potential energy increasing, decreasing or remaining constant? (Hint: take a look at the definition of potential energy in the table on page 1.)

j) Is the total energy increasing, decreasing or constant?

The last prediction focused solely on the interval when the girl was riding down the incline. The next two predictions will ask you to tabulate answers about all the portions of the girl’s motion. Ask yourself the questions from the last prediction to complete the following predictions.

Prediction 2 Indicate whether each of the following are positive, negative or zero by writing

a ‘+’, ‘–’ or ‘0’ in each cell of the table.

KE PEg Etotal The girl starts out at rest at the top of the track

The girl is riding down the track

The girl is at the bottom of the

track

The girl is riding up the other side

of the track

The girl reaches the top of the

other side of the track

Prediction 3 Complete each cell by indicating whether each quantity is increasing (I),

decreasing (D), constant (C), a maximum (Max) or a minimum (Min).

KE PEg Etotal The girl starts out at rest at the top

of the track

The girl is riding down the track

The girl is at the bottom of the

track

The girl is riding up the other side

of the track

The girl reaches the top of the

other side of the track

©2020 by Heidi Van Tassell Mesa Community College Page 4.1.5

Mesa, Arizona 85202

Computer 1. Open the PhET simulation at

Procedure

skate-park_all.html

1. Click on the “Intro” button. 3. Click the option “Pie Chart” on the right-hand side of the page. 4. Make sure Friction is set to “None”. 5. Make sure Gravity is set to “Earth” or “9.8m/s2.” 6. Click on “Slow Motion” button at the bottom of the page. 7. Click and drag the girl to the top of the track. Release her and observe

the pie chart as she skates down the track and back up the other side.

Question 3 What type of energy does the girl have when she is located at the top of the track?

Question 4 What type of energy does the girl have when she is located at the bottom of the track?

Question 5 What happens to the total energy as the girl skates up and down the hill? Does it

increase, decrease or remain constant?

1. At the bottom of the page click the “Measure” button. 9. Once again click and drag the girl to the top of the track. Release her

and observe the purple dots that remain in her track after she passes.

These are places where we can measure data.

1. Pause the simulation when the girl is at the top of the track and the purple dots are located all over the track.
2. Move the measuring tool over the top of one of the purple dots. Data should appear in the connected box for potential energy, kinetic

energy, thermal energy (which is work done by friction) and total

energy.

1. Move the measuring device to different purple dots to allow you to answer the following questions:

Question 6 Indicate whether each of the following are positive, negative or zero by writing

a ‘+’, ‘–’ or ‘0’ in each cell of the table.

KE PEg Etotal The girl starts out at rest at the top

of the track

The girl is riding down the track

The girl is at the bottom of the

track

The girl is riding up the other side

of the track

The girl reaches the top of the

other side of the track

Question 7 Complete each cell by indicating whether each quantity is increasing (I),

decreasing (D), constant (C), a maximum (Max) or a minimum (Min).

KE PEg Etotal The girl starts out at rest at the top

of the track

The girl is riding down the track

The girl is at the bottom of the

track

The girl is riding up the other side

of the track

The girl reaches the top of the

other side of the track

You should have noticed these are the same questions that you answered

in predictions 1 & 2.

Experiment 2: Next consider the situation shown at right that

involves a girl skateboarding on a track with

friction. The girl rides down the hill, reaches the

bottom, rises on the other side of the track, turns

around, then rides down the hill once again.

Assume the system consists of the girl, her

skateboard, and the earth. The track is a part of

the environment, not a part of the system.

Computer

Procedure 1. Click on the “Measure” button at the page.

1. Make sure Friction is set halfway between “None” and “Lots.” 3. Make sure Gravity is set to “Earth” or “9.8m/s2.” 4. Click on “Slow Motion” button at the bottom of the page. 5. Once again click and drag the girl to the top of the track. Release her

and observe the purple dots that remain in her track after she passes.

These are places where we can measure data.

1. Pause the simulation when the girl is at her highest point on the opposite side of the track.
2. Move the measuring tool over the top of one of the purple dots. Data should appear in the connected box for potential energy, kinetic

energy, thermal energy (which is work done by friction) and total

energy.

1. Move the measuring device to different purple dots to allow you to answer the following questions:

Question 8 Write down the value (amount) of energy for each cell of the table.

KE PEg Thermal E The girl starts out at rest at the top

of the track

The girl is riding down the track

The girl is at the bottom of the

track

The girl is riding up the other side

of the track

The girl reaches the top of the

other side of the track

Question 9 The girl started at a height of 6 meters on one side of the track. How high did

she get on the other side of the track?

Question 10 Why did the girl not reach as high of a height on the other side of the track?

The column labeled Thermal Energy represents the work done by friction

on our system. Since we have chosen NOT to include the track in our

system, this is work done by an outside force and thus is a loss of energy

to out system. When we calculate the total energy for our system, this

value should NOT be included. Copy over the potential and kinetic values

from Question 8 and add them together to find the total energy for our

system at each point.

Question 11 Write down the value (amount) of energy for each cell of the table.

KE PEg

Total

Energy The girl starts out at rest at the top

of the track

The girl is riding down the track

The girl is at the bottom of the track

The girl is riding up the other side of the track

The girl reaches the top of the other side of the track

Question 12 Is the total mechanical energy of our system increasing, decreasing or remaining constant?

Question 13 Using your own words write a sentence or two explaining the conservation of energy for any system.

Last Updated on September 24, 2020 by Essay Pro