Investigating Force and Energy

IntroductionAll life depends upon energy which allows us to move and interact with our environment. Formally energy is

defined as the ability or capacity to do work. Most of the energy on the earth comes from the sun. The sun's rays are needed so that plants can make food. Animals and human beings use the energy found in food to operate their bodies and muscles. The sun's energy is also stored in coal, wood, and oil, which are burnt to do work.

All energy originates from four fundamental forces: strong nuclear forces, weak nuclear forces, gravitational forces, and electromagnetic forces. We find that these fundamental forces act to produce common forms of energy in our environment. These forms include: thermal, light, sound, mechanical, electrical, chemical, and nuclear.

People often confuse energy, force, work, and power. Force is a push or a pull on an object. Energy is the ability to do work. Work and energy are measured in the same units. The amount of work is determined by the strength of the force used to move an object and the distance the object moves. Power measures the rate at which work is done.

In this activity we will explore the various ways energy is transferred to an object that result in changing its motion. This motion will be observed as a”race” between two marbles. The winner of the race did so because of possessing more energy. Was greater energy transferred to the winning marble due to its mass, starting height, or diameter? In the following activities we will answer these questions.

Objectives for this Unit1. Given the following list of terms, identify each term's correct definition.

Conversely, given definitions identify their correct terms. Acceleration, force, kinetic energy, mass, potential energy, kinetic energy

2. Identify or describe the four fundamental forces and the forms of energy they produce.

3. Given the formula for Newton’s second law, f = m X a, describe how acceleration depends upon the relationship between mass of the object and the force applied

4. Identify or describe the two types of energy and given the formula for potential energy P.E. = m x g x h, explain the formula.

5. Identify the affect of position/height on the energy of an object6. Identify the affect of mass on the energy of an object

MaterialsInclined plane, ramp, Meter stick, Newton scale, Various Marbles:

Diameter (cm) Mass (g) Mass (kg) Description 1- 2.54 12.5 0.0125 Rubber Ball1- 2.54 66.8 0.0668 Steel Ball2 - 2.54 20.0 0.0200 Yellow Glass2 - 1.50 0.51 0.0051 Blue Glass

Types of EnergyThe various forms of energy can be exhibited as two types, potential and kinetic energy. Potential is the amount of

stored energy and kinetic is the dynamic or energy due to the motion of the object. Potential energy is the energy stored by an object as a result of its position or the position of its parts. A rock on a

table, a bowl of cereal, a stick of dynamite, and a tank of gasoline are all examples of objects that have energy stored in atoms or molecules. The rock has potential energy because of its height that can be released and converted to kinetic energy and heat, if it is dropped.

Potential Energy = mass x acceleration of gravity x height or P.E. = m x g x hWhere:

P.E. = potential energy is equal to force (force = mass x acceleration) multiplied by distance. The result is a unit of measurement labeled newton-meters. 1 newton-meter is a unit called a joule.

m = the mass of the object being considered

g = The acceleration of gravity on planet Earth, 9.8 meters / second2. (i.e. an object that is dropped will

accelerate at a rate of 9.8 m/sec2)h = height in meters that the object falls.

Investigating Force and Energy ©2009 Page 1

Kinetic energy is the dynamic energy that matter has because of its motion and mass. Moving cars, a falling rock, a bullet shot from a gun or a flow of electrons are all examples of kinetic energy.

Kinetic Energy = ½ mass x velocity2 or K.E. = ½ m x v2

Where:K.E. = the energy that a body possesses as a result of its mass and velocity. The result is a unit of

measurement labeled newton-meters. 1 newton-meter is a unit called a joule. m = the mass of the object moved and would be measured in Kilograms.v = the velocity measured in meters per second.

Force and Energy ActivitiesIn the following activities two objects will race each other down an inclined plane. Our investigations are to discover what characteristics can be used to determine the winner of the race. (Predict the future)

Section 1: Measuring the Force When an object moves, some form of energy was transferred imparting a force to the object causing the movement. A change in movement or velocity of the object is referred to as acceleration. As Newton described in his second law the amount of acceleration depends upon the relationship between mass of the object and the force applied to the object. The following is a statement of this relationship.

force = mass X acceleration or f = m X aWhere:

f = The force (a push or a pull) that tends to produce an acceleration of some mass in the direction of its application measured in Kg - meters / sec2 is a unit of measurement called a newton. (Note: 4.5 newton is approximately 1 pound).

m = the mass of the object moved (measured in Kilograms).

a = the acceleration of the object that moved and is an indication of a change in velocity over a period of time. Acceleration (measured in meters / second2).

A push or a pull is considered a force. The strength of a force is measured in newtons and is described by Newton’s second law f = m x a where “f” is force, “m” is mass measured in kilograms, and “a” is the acceleration due to gravity. The purpose of the inclined planes is to supply that force for our racers. We could measure the force applied to the racers with a newton scale by simply attaching the scale to our racers while they are on the ramp. We could also calculate the force based upon the mass of the racers and their placement on the ramp. The forces for each racer based upon their position on the ramp will be found in table 1. Look at these forces carefully and answer the following question.

1. How does the force change due to a change in the mass?2. What does the amount of force depend?

Section 2: Which One “Wins”?In the following activities you will race two marbles to determine which crosses the finish line first. To be declared the winner a marble must win by at least the diameter of the marble. It must be a “clear” winner or we will declare a tie.

1. Place a piece of tape for the “start” line and lineup the end/bottom of the ramps with the “start line”.

2. Place a piece of tape for a finish line 50.0-cm. from the start line. Adjust the ramps to any height, but the same height. (see chart)

3. Select two marbles with the same mass and diameter and place them on the starting point at the top of the ramps.

4. Release them at the same instant and observe the outcome of the “race”.

5. Select another two marbles with the same mass and diameter and repeat the race.

6. Complete the statement: When two marbles that are the same “race” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Finish Line

50.00-cm

25.00-cm

Section 3: Changing the Height of the RacerIn this activity we will keep the release position and the mass of the marble constant while varying the height.

1. Predict (P) the winning ramp for each race.2. Adjust the ramps to the height indicated in the table for position 1.3. Select two large marbles with the same mass (20.0-g or .02-Kg) and diameter. Obtain the force for the marbles from

table 1 and record.4. Place one marbles on the ramp A one marbles on the ramp B and then release them at the same instant and observe

the outcome of the “race”. Repeat three times to verify the results. Record the actual winner (A).5. Repeat the above procedure for each of the other heights indicated in the table.6. Calculate the Potential Energy for each race.

Ramp A Ramp BWinning

Ramp

Heightmeters

ForceNewtons

P.E.P.E. = m x g x h

Joules

Heightmeters

ForceNewtons

P.E.P.E. = m x g x h

JoulesP A

Position 1 0.03 0.03

Position 2 0.03 0.06

Position 3 0.03 0.09

7. Does the change in height effect speed of the marble to cross the finish line? Why?

8. If energy is the “ability to do work” does the change in height affect energy? (Explain fully)

Section 4: Changing the Mass of the RacerIn this activity we will keep the release position and the height of the marble constant while varying the mass .

1. Predict (P) the winning ramp for each race.2. Place the two ramps at the 0.06-m height. You will leave them at this height for the entire experiment.3. Select marbles mass 1 (mass as indicated in the table). Obtain the force for the marbles from table 1 and record.4. Place the marbles on the ramps then release them at the same instant and observe the outcome of the “race”. Repeat

three times to verify the results. Record the actual winner (A).5. Repeat the above procedure for each of the other masses indicated in the table.6. Calculate the Potential Energy for each race.

Ramp A Ramp BWinning

Ramp

Mass

(Kilogram)

Force

Newtons

P.E.

P.E. = m x g x h

Joules

Mass

(Kilogram)

Force

Newtons

P.E.

P.E. = m x g x h

Joules

P A

Mass 1 0.0051 0.0051

Mass 2 0.0051 0.0120

Mass 3 0.0051 0.0200

Mass 4 0.0051 0.0668

7. Does the change in mass effect speed of the marble to cross the finish line? Why?

8. If energy is the “ability to do work” does the change in mass affect energy? (Explain fully)

Instructors Note:We have learned how the factors of height, mass, and force interact. There is one activity that will help clarify the relationship. In the above activities our racecourse was 50.00-cm. which works well for desktops but does not let us “see” all the energy in the racers. Place the ramps on the floor and repeat the previous experiments this time allowing the racers to “run” as far as they can. This will “use up” (convert to motion) all the energy and we will observe which one went the farthest or had the most energy.

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Energy and Work Activities Work is defined as the expenditure of energy that occurs when a force is used to move an object through a given distance. A quantitative measure of work is determined by the product of the force acting and the distance moved in the direction the force acts:

work = force x distance or w = f x d

Section 5: The Affect of Height on Energy and WorkIn this activity we will use only one ramp and keep the release position, top of ramp, and the mass of the marble constant while varying the height. We will place a barrier at the end of the ramp which we will know the force needed to move it. Based upon our previous experiments we learned which condition produced the most energy and therefore which condition should result in the barrier being moved the farthest. We can measure this distance and with the force needed to move the barrier we can calculate the work done by moving the barrier. (w = f x d)

1. Adjust the ramp to the height indicated in the table.

2. Select one 0.0051 kg marble. Obtain the force for the marble from table 1 and record.

3. Place the marble on the ramp, then release it and measure the distance the barrier was moved using the grid provided. Repeat three times to verify the results. Place the ramp on the grid. Mark the zero point of the barrier and measure how far the barrier moves.

4. Repeat the above procedure for each of the other heights indicated in the table.

5. Calculate the potential energy of the marble using P.E. = m x g x h.

Where:

m = mass in kilograms

g = force of gravity 9.8 m/sec2

h = height object dropped (marble) in meters

6. Calculate work done using w = f x d.

Where:

f = force in newtons.

d = distance barrier moved measured in meters.

“Marble”/Object 1.5-cm Barrier

Height

(meters)

Mass

(Kilogram)

Potential Energy

P.E. = m x g x h

(Joule)

Force

Needed to move

(Newton)

Distance

(Meter)

Work

w = f x d

(joule)

Position 1 0.03-m

Position 2 0.06-m

Position 3 0.09-m

7. Does the change in height affect the potential energy? If it does, how?

8. If energy is the “ability to do work” does the change in height affect energy? (Explain fully)

9. Why isn’t work equal to potential energy?

Investigating Force and Energy ©2009 Page 4

Section 6: The Affect of Mass Energy and on WorkIn this activity we will use only one ramp and keep the release position, top of ramp, and the height of the marble constant while varying the mass. We will place a barrier at the end of the ramp which we will know the force needed to move it. Based upon our previous experiments we learned which condition produced the most energy and therefore which condition should result in the barrier being moved the farthest. We can measure this distance and with the force needed to move the barrier we can calculate the work done by moving the barrier. (w = f x d)

1. Adjust the ramp to the height indicated in the table.

2. Select one marble (mass 1). Obtain the force for the marbles from table 1 and record.

3. Place the marble on the ramp, then release it and measure the distance the barrier was moved using the grid provided. Repeat three times to verify the results.

4. Repeat the above procedure for each of the other masses indicated in the table.

5. Calculate the potential energy of the marble using P.E. = m x g x h.

6. Calculate work done using w = f x d.

“Marble”/Object Barrier

Height

(meters)

Mass

(Kilogram)

Potential Energy

P.E. = m x g x h

(joule)

Force

Needed to move

(newton)

Distance

(meter)

Work

w = f x d

(joule)

Mass 1 0.03

Mass 2 0.03

Mass 3 0.03

7. Does the change in mass affect the potential energy? If it does, how?

8. If energy is the “ability to do work” does the change in mass affect energy? (Explain fully)

9. Why isn’t work equal to potential energy?

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Table 1 – Physical Properties of “Marbles”

Physical Properties Calculated Force in Newtons Due to Angle

DescriptionDiameter

(cm)Mass

(kilogram)3.00-cm 6.00-cm 9.00-cm Vertical

Steel 2.54 0.0668 0.08 0.16 0.24 0.66

Yellow Glass 2.54 0.0200 0.02 0.05 0.07 0.19

Yellow Glass 2.54 0.0200 0.02 0.05 0.07 0.19

Yellow Glass-B 2.54 0.0185 0.02 0.04 0.06 0.18

Yellow Glass-B 2.54 0.0185 0.02 0.04 0.06 0.18

Rubber Ball 2.54 0.0125 0.015 0.03 0.045 0.1225

Blue Glass 1.50 0.0051 0.006 0.0122 0.0184 0.0499

Blue Glass 1.50 0.0051 0.006 0.0122 0.0184 0.0499

-- -- -- -- Suggest We Remove

To convert grams to newtons:1. Change grams to Kilograms2. Calculate newtons f = m x a

Where “a” is acceleration due to the force of gravity (9.8 m/sec2) and m is the mass in kilograms

Investigating Force and Energy ©2009 Page 6

F11

F11

F_l_

h

Wt

25.00-cm

sin α = h / 25.00

F11 = Wt x sin α

α α