How To Find Kinetic Energy From Potential Energy

Energy Transfer Experiment: Gravitational Potential Energy to Kinetic Energy

Does a falling object have potential energy or kinetic energy or both? In other potential free energy experiments, nosotros demonstrated the Police force of Conservation of Free energy: energy tin neither exist created nor destroyed, but instead, energy transfers from ane course to some other. In this investigation, we will have a look at the role of gravity in energy transfer. This investigation aligns with NGSS MS-PS3-ane and MS-PS3-five and can be scaled upwardly for high schoolhouse students to address HS-PS3-1 and HS-PS3-2.

NGSS Alignment: MS-PS3-1

The disciplinary cadre thought behind this standard is PS2.A: Definitions of Energy. It specifically looks at energy in move (kinetic free energy) and its relationship with the mass of the object in motion and the speed of the object. In the setup of the lab, students use a cart traveling downwardly to exam how changing the cart's irresolute speed will impact its kinetic energy and how changing the mass of the cart will modify its kinetic energy. A PocketLab Voyager is placed on either the cycle of the cart or directly on top of the cart, in order to measure its speed every bit information technology travels downwards a ramp.

At dissimilar points down the ramp, students summate the gravitational potential free energy and the kinetic free energy of the cart. In their calculations they will sympathize the relationship between GPE and KE, helping them with a deeper understanding of concepts in energy conservation, and Crosscutting Concepts, Scale Proportion, and Quantity. Int he crosscutting concepts (specifically how mass and velocity relate to kinetic energy and how mass and height relate to gravitational potential free energy). For every run, students must use the Science and Engineering Practise, Analyzing and Interpreting Information, to procedure how the changing variables affect the collected velocity data and the calculated kinetic free energy information. In the information assay, students must too bear witness in tables and graphs how the potential and kinetic energy changes in relation to the distance the cart has traveled, the speed of the cart, and the mass of the cart.

MS-PS2-2: Construct and translate graphical displays of data to draw the human relationship between kinetic energy to the mass of an object and the speed of the object.

The standard is broken down into the three NGSS pillars below:
Science and Engineering Practices  - Analyzing and Interpreting Information
Disciplinary Core Ideas  - PS3.A Definitions of Energy
Crosscutting Concepts  - Scale, Proportion, and Quantity

Introduction

Potential energy is energy that is stored in an object. Potential energy can transfer into other forms of free energy like kinetic energy. Kinetic energy is energy an object has because of its motion.

A ball held in the air, for case, has gravitational potential energy. If released, every bit the brawl moves faster and faster toward the basis, the strength of gravity volition transfer the potential free energy to kinetic energy. The higher the ball, the more gravitational potential energy -- it will autumn longer and faster as it accelerates toward the world.

Now, if two balls are dropped from the same height, just one has more mass, which brawl will require more than energy to finish? Which ball, therefore, has more kinetic free energy?

We can show this with a science experiment using your PocketLab.

Objective

In this experiment, students will:

1. Gather evidence and information to back up the Constabulary of Conservation of Energy.
2. Collect information to summate the corporeality of energy in a system at dissimilar moments.
3. Determine how the total energy in a system is cleaved upwardly into different types of energy at different moments and how that is related to the law of conservation of energy.
4. Decide how the mass of a cart affects its gravitational potential energy and kinetic energy every bit information technology rolls down a ramp.

Materials

1. Sensor: PocketLab Voyager or PocketLab 1
2. Cart: PocketLab HotRod, cart kit, physics cart, Hot Wheels car, or any other small toy automobile
3. Ramp, homemade or available as a kit with adjustable angle
4. Mass gear up
5. Calibration
6. Measuring tape

Formulas and Key Words

Define the following:

• Gravitational Potential Energy (GPE)
• Kinetic Free energy (KE)
• Velocity (five)
• Law of Conservation of Energy
• Total Energy (TE)
• Thermal Energy (Therm E)
• Friction

Formulas for lab:

GPE = mgh
KE = ½ mv^2

Hypothesis

Write a prediction to answer the following question: If the mass of the cart is increased, how will the cart's GPE, KE, TE, and Velocity exist affected as the cart rolls down the ramp?  Explain your hypothesis with either background cognition about energy, forces, and motion and/or data gathered in the introduction and diagrams below.

Procedure

To measure position and velocity, apply either the VelocityLab App (PocketLab One or PocketLab Voyager) or the infrared rangefinder sensor (PocketLab Voyager but).

Infrared Rangefinder (PocketLab Voyager)

Follow the steps below:

• Get to the PocketLab Spider web App (in a Chrome browser) using the following address: thepocketlab.com/app or open up up the PocketLab mobile app.
• For instruction on how to employ the PocketLab Web App go hither.
• Click on the "Alter Graph" icon. Click "Rangefinder" and "Rangefinder Velocity".
• When setting upward your cart and ramp, you'll need to make sure the rangefinder has a "wall" (a cardboard box will do) at the bottom of the ramp to give the rangefinder a clear betoken.

Example of PocketLab Voyager on cart measuring position and velocity with IR Rangefinder at different points down the ramp

VelocityLab App (PocketLab Voyager or PocketLab I)

Follow the steps below:

• Go to the VelocityLab Web App (in a Chrome browser) using the following address: thepocketlab.com/app and on the first menu click on the "Connect to VelocityLab" push. On iOS, use the VelocityLab app available in the App Store.
• Turn on the PocketLab Voyager past clicking the button on the pinnacle.
• For instruction on how to use the PocketLab Web App get here
• Follow the prompts on the VelocityLab setup wizard.
• Click on the "Change Graph" icon. Click to view "Position" and "Velocity".

Case of PocketLab on cart measuring position and velocity at dissimilar points downwardly a ramp with PocketLab's VelocityLab App

Collecting Testify (Data and Observation)

Control Variables for Every Run

For every new run, you volition modify the contained variable merely go on a set of control variables the same. This is to make sure the experiment is accurate. Record these control variables below:

Control Variables
Angle of ramp
Height of cart at top of ramp
Distance cart volition travel down the ramp

Independent Variables for Every Run
For every run you will exist testing an independent variable. You will change the value o this variable to see how the alter affects your dependent variables, measured in your data and seen in your observations.

Contained Variable

Mass of cart

Data Collection for Run 1
Find the mass of the cart with the PocketLab attached and record it as the value of your Independent Variable for Run i.

Independent Variable
Mass of cart

Run 1 Observations

• Set up the cart at the tiptop of the ramp according to your control variables
• Brainstorm recording data for Trial one.
• Curl the cart down the ramp.
• Use the data to fill up out the following table for Trial 1
• Repeat steps for Trials 2 and 3.
• Tape any overall observations in the Run 1: Observations section higher up.

Run one - Trial 1
Peak of cart (m)
Displacement (m)
Velocity (k/southward)
GPE (J)
KE (J)

Run i - Trial ii
Height of cart (m)
Displacement (m)
Velocity (m/due south)
GPE (J)
KE (J)

Run 1 - Trial 3
Height of cart (m)
Displacement (m)
Velocity (one thousand/s)
GPE (J)
KE (J)

Data Collection for Run 2

Add a mass from your mass fix to the cart. Find the new mass of the cart with PocketLab and added mass and record it as the value of your Independent Variable for Run ii.

Contained Variable
Mass of cart

Run two Observations

• Prepare the cart at the top of the ramp according to your command variables
• Begin recording data for Trial ane.
• Whorl the cart down the ramp.
• Utilize the data to fill out the following table for Trial i
• Repeat steps for Trials 2 and 3.
• Record any overall observations in the Run 2: Observations section higher up.

Run 2 - Trial ane
Height of cart (k)
Displacement (m)
Velocity (m/s)
GPE (J)
KE (J)

Run two - Trial 2
Pinnacle of cart (k)
Displacement (m)
Velocity (m/s)
GPE (J)
KE (J)

Run 2 - Trial 3
Meridian of cart (yard)
Displacement (m)
Velocity (m/s)
GPE (J)
KE (J)

Data Collection for Run 3

Add a mass from your mass set to the cart. Find the new mass of the cart with PocketLab and added mass and record information technology equally the value of your Independent Variable for Run iii.

Independent Variable
Mass of cart

Run 3 Observations

• Set up the cart at the meridian of the ramp according to your control variables
• Begin recording data for Trial i.
• Roll the cart down the ramp.-Use the data to fill out the following table for Trial 1
• Echo steps for Trials 2 and iii.
• Tape any overall observations in the Run 3: Observations section above.

Run three - Trial 1
Height of cart (m)
Displacement (thou)
Velocity (k/s)
GPE (J)
KE (J)

Run three - Trial 2
Height of cart (m)
Displacement (thousand)
Velocity (m/s)
GPE (J)
KE (J)

Run 3 - Trial 3
Elevation of cart (1000)
Displacement (yard)
Velocity (m/s)
GPE (J)
KE (J)

Information Analysis

Average the trials from each run below. Get out the bottom 2 rows of each tabular array empty for now.

Run 1 Average
Height of cart (m)
Deportation (m)
Velocity (grand/s)
GPE (J)
KE (J)

Run 2 Boilerplate
Summit of cart (thou)
Displacement (g)
Velocity (m/s)
GPE (J)
KE (J)

Run 3 Boilerplate
Tiptop of cart (m)
Displacement (m)
Velocity (m/s)
GPE (J)
KE (J)

Information Analysis Questions

• Wait at the average data for Run ane. Add the GPE and KE at every location. Is the total free energy of the system equal to just the GPE plus the KE? If that is the case, what is happening to the full energy in the organisation? Does this match the Police of Conservation of Free energy? Explain.
• Something is missing in this information model. Look dorsum at the formulas and keywords. Explain what is missing and how information technology relates to the Constabulary of Conservation of Energy.
• Using the averages for each run, detect the missing data and add it to the information tables above. Now discover the full energy (TE) in the organisation at each point and add it to the information tables also. Utilise the empty rows to add the new data.
• Describe a series of bar graphs for each Run Boilerplate showing the distribution of free energy and total energy at each location on the ramp.
• Looking at the bar graphs, what pattern practise you detect?
• Did the average velocity for each location change much betwixt the runs?
  

Conclusion and Lab Report

Option ane: Write a concluding paragraph that answers the Conclusion Questions at the bottom of the page.
Choice 2: Write a full lab written report for this lab activeness. A lab study is a peachy way to summarize how y'all conducted your experiment and tested your hypothesis, the data collected, and any conclusions you can draw most the scientific question that was tested. In your lab report include:

1. Your original hypothesis from the beginning of the lab (in this case a description of your sketches).
2. The objectives or scientific questions you lot wanted to answer with the lab activity
3. What materials you used in the experiment.
4. A detailed description of how the lab was gear up and how yous tested your hypothesis.
5. A summary of your data and the answers to your information analysis questions.
6. Any observations you lot made with your group.
7. A conclusion that answers the Decision Questions below.

Determination Questions

• Look back at your hypothesis from the beginning of the lab. Was your hypothesis was valid or invalid? Why or why not? Back up your respond with information/evidence collected from the lab experiment and scientific reasoning nearly energy, forces, and motion.
• GPE: Describe the relationship betwixt an object'south summit and its gravitational potential energy? Did y'all run across evidence of this relationship in data collected? Explain.
• GPE: Describe the relationship between an object'southward mass and its gravitational potential energy? Did you lot run into testify of this human relationship in data collected? Explain.
• KE: Describe the relationship between an object's mass and its kinetic free energy? Did you see evidence of this relationship in data collected? Explain.
• KE: Draw the human relationship between an object's velocity and its kinetic energy? Did you see bear witness of this relationship in data collected? Explicate.
• Velocity: In the today's scenario, depict the relationship between an object'due south mass and its velocity? Did you lot see evidence of this relationship in data collected? Explain.
• Velocity and KE: Recollect about a big bus and a small car traveling at the aforementioned velocity. Which vehicle can do more harm in a crash? Explain your answer using data collected in today's lab activity.
• Thermal Energy: Rub your hands together slowly for 10 seconds and and then place your palms on your face. Rub your hands together quickly for 10 seconds and identify your palms on your face up. Do you feel a difference in thermal energy? How does this relate to the kinetic free energy of the cart and the thermal free energy produced in the system? Explain.
• Thinking especially about the bar graphs drawn in the data analysis department, did the data/evidence collected and observations made during the lab activity support the law of conservation of energy? Explain.

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Example Student Lab Report and Information

Hypothesis

If the mass of the cart increases, I predict the cart's GPE, KE, TE, and Velocity will all increase. I believe the added mass will make the cart become faster down the ramp which will also crusade the KE of the cart to increment because KE = 1/two mv^ii. I believe the GPE will increase considering the equation for GPE (GPE = mgh) shows that increasing either the mass or the acme of the object will increase the GPE. I believe the TE of the cart will increment because both the GPE and KE will increment.

Objectives

1. Assemble prove and data to support the Law of Conservation of Free energy.
2. Collect data to calculate the amount of energy in a arrangement at different moments.
3. Determine how the total energy in a organisation is broken up into different types of energy at dissimilar moments and how that is related to the Law of Conservation of Energy.
4. Determine how the mass of a cart affects its gravitational potential energy and kinetic energy every bit information technology rolls downwards a ramp.

Materials

1. PocketLab Voyager
2. PocketLab HotRod
3. Ramp
4. Mass set
5. Scale
6. Measuring tape

Description

Using PocketLab Voyager and the VelocityLab App, nosotros ran the cart down the ramp starting .50 k up the ramp. The height of the cart (measured direct from the footing) at .50 thousand up the ramp was 0.12 thousand. One quarter of the manner down the ramp, the height of the cart was 0.08 m, 1/2 downward the ramp it was .06 m, three/iv of the style down the ramp it was 0.03m, and all the fashion down the ramp was 0.0 one thousand. This information, along with the mass of the cart was used to summate the GPE of the cart at unlike locations. Using the Position and Velocity information from VelocityLab, we found the velocity of the cart one/4, 1/ii, 3/4, and all the manner downwards the ramp. This was used to calculate the KE of the cart. We conducted three runs for this experiment. At each run nosotros increased the mass of the cart to come across how information technology affected the GPE, KE, Velocity, and TE of the cart. For each run we conducted three trials and averaged our results. For our "Resultant Visualization" we compared the increase in the cart's mass to the average KE of the cart at the lesser of the ramp for each run.

Collecting Testify: Data and Observations

Run ane

Independent Variable
Mass of cart	0.176 kg

Run 1 Observations The velocity data 1/four, i/2, 3/4, and all the mode downward the ramp were adequately consistent across the three trials. The GPE of the cart was the same across trials. The KE of the cart was also consistent across trials. The resultant data listed here is the average pinnacle KE at the bottom of the ramp across all iii trials. Resultant for Information Visualization: KE at lesser of ramp = 0.071 J

Run 1 Trial iii (Velocity at bottom of ramp = 0.90 grand/southward)

Run 2

Independent Variable
Mass of cart	0.215 kg

Run two Observations Every bit the cart traveled down the ramp, we noticed that the velocities at different points didn't change much from the data in Trial ane. The added mass didn't seem to take an touch on on the velocity of the cart as it went downwardly the ramp. The Kinetic Free energy calculated increased, only that seemed to be a event of the increasing mass in the equation, not an increase in Velocity. The resultant shows the average Kinetic Free energy of the cart at the bottom of the ramp. Resultant for Data Visualization: KE at bottom of ramp = 0.092 J

Run 2 Trial iii (Velocity at bottom of ramp = 0.94 one thousand/south)

Run iii

Independent Variable
Mass of cart	0.258 kg

Run 3 Observations Like to Run 2, the added mass did not bear on the velocity of the cart at any point. The GPE and KE of the cart increased every bit the mass increased compared with Runs 1 and 2. The resultant data is the boilerplate KE of the cart at the bottom of the ramp. Resultant for Data Visualization: KE at lesser of ramp = 0.111 J

Run iii Trial 3 (Velocity at lesser of ramp = 0.95 m/due south)

Information Assay

We averaged our results beyond all trials for each run. The results are in our included data tables. When looking at the average data for Run one, we determined that adding the GPE and KE at every location did non give us the Total Energy in the system. Data was missing. The total energy should stay the same throughout the cart's trip downwards the ramp, because energy does not just disappear. It can change grade only not be destroyed. This means some of the GPE was not just transferring to KE. Some was likewise transferring to another type of energy.

Looking dorsum at our Key Words from the offset of the lab, we determined some of the energy was transferring to Thermal Free energy through the process of Friction. Past subtracting the GPE and the KE from what should exist the Total Energy at each location nosotros were able to determine an approximate value for the Thermal Energy at each location. We added this to our information tables for each Run average.

Nosotros then drew bar graphs breaking down the type of energy at each location for each of the Run averages. We noticed that no affair what, the bar graph for Full Energy was always equal to the sum of the bar graphs for GPE, KE, and Thermal Energy. The values of those bar graphs inverse between those three types of free energy, but their sum was always the aforementioned. When the mass increased in Runs 2 and 3, the Total Energy increased, only the blueprint shown in the bar graphs was the aforementioned. Increasing mass had no effect on velocity data however.

Run 1 Boilerplate
Height of cart (thousand)	0.12	0.08	0.06	0.03	0.00
Displacement (one thousand)	0.000	0.123	0.253	0.737	0.500
Velocity (one thousand/s)	0	0.433	0.650	0.787	0.900
GPE (J)	0.207	0.138	0.103	0.052	0.000
KE (J)	0.000	0.017	0.037	0.054	0.071
Therm. Energy (J)	0.000	0.052	0.067	0.101	0.136
Total Energy	0.207	0.207	0.207	0.207	0.207

Run 2 Boilerplate
Height of cart (1000)	0.12	0.08	0.06	0.03	0.00
Deportation (m)	0.000	0.123	0.253	0.377	0.503
Velocity (m/s)	0.000	0.453	0.663	0.813	0.927
GPE (J)	0.253	0.169	0.126	0.063	0.000
KE (J)	0.000	0.022	0.047	0.071	0.092
Therm. Energy (J)	0.000	0.062	0.080	0.119	0.161
Total Energy	0.253	0.253	0.253	0.253	0.253

Run 3 Average
Height of cart (m)	0.12	0.08	0.06	0.03	0.00
Deportation (m)	0.000	0.123	0.257	0.373	0.500
Velocity (m/s)	0.000	0.457	0.667	0.810	0.927
GPE (J)	0.303	0.202	0.152	0.076	0.000
KE (J)	0.000	0.027	0.057	0.085	0.192
Therm. Energy (J)	0.000	0.074	0.121	0.142	0.192
Total Energy	0.303	0.303	0.303	0.303	0.303

Resultant Data Visualization: Mass of the cart compared to average Kinetic Free energy of the cart at the bottom of the ramp.

Conclusion

After examining the information, parts of our hypothesis from the start of the lab are invalid while some parts are valid. Nosotros predicted that increasing the mass would increase the velocity of the cart and the KE of the cart. Increasing the mass of the cart had no effect on the velocity of the cart, and while the KE did increase, this was because of the increase in mass, not an increment in velocity, which is what we predicted. We believe the increased mass of the cart had no result on the velocity because gravity accelerates all objects virtually Globe'due south surface at approximately the same rate, regardless of mass. We were correct in predicting that the increase in mass would increase the GPE of the cart because increasing either mass or height increases GPE. We were also correct in predicting that the Full Energy would increment because of the increase in GPE.

Source: https://archive.thepocketlab.com/educators/lesson/potential-energy-kinetic-energy-experiment-gravity

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