Understanding Energy Conservation: Kinetic and Potential Lab
School
Southern Illinois University, Carbondale**We aren't endorsed by this school
Course
PHYS 205
Subject
Physics
Date
Dec 11, 2024
Pages
12
Uploaded by MegaWorld15628
Lab 9: Conservation of EnergyPre-lab Questions:1.The higher above the ground an object is located, the more ____________ (potential/kinetic) energy the object has. The faster an object is moving, the more ____________ (potential/kinetic) energy the object has. 2.Figure 1 shows a snowboarder on a hill. The snowboarder starts from rest at the top of the hill, and then he moves down the hill without any braking or slowing down. For each position (A, B, and C) on the hill, determine if the snowboarder has: * only potential energy * only kinetic energy * both potential and kinetic energy 3.Assuming there is no friction on the hill in Figure 1, is the amount of total energy at location A higher than, lower than, or the same as the amount of total energy at location C? Explain. 4.What is thermal energy, and when does it need to be considered? 5.How many track pieces are needed to build the lab setup? 6.What is the difference between part 1 and part 2 of this lab? 7.How many sets of data are collected for each different scenario in the lab? (How many trials?) Figure 1: Snowboarder sliding down a hill with no braking and no friction.
Objective•Understand the principle of conservation of energy. •Apply the principle to situations involving gravitational potential energy and kinetic energy. •Use conservation of energy to make testable predictions. ApparatusPAScar Smart Cart, two 1.2 m Dynamics Tracks, Stand, Balance or Scale IntroductionIn this lab, you will be focused on two different types of energy. Kinetic energyis the energy of motion; the faster an object moves, the more kinetic energy it has. The kinetic energy of any object of mass m moving with a velocity v can be calculated using ࠵?࠵? =!"࠵?࠵?". (Equation 1) Gravitational potential energyis energy stored in an object due to its position (or height); the higher an object is located, the more potential energy it has. The potential energy of an object of mass m located at a height of h can be calculated as ࠵?࠵? = ࠵?࠵?ℎ, (Equation 2) where g is the acceleration due to gravity. It is important to note that the height in this equation is the difference in height between the location of the object and the surface that the object can fall onto. There are other forms of energy beyond kinetic and potential energy. For example, thermal energymanifests as heat and can be generated in a situation where friction is involved. Light is also a form of energy. Using the concept of energy to determine an object’s motion is much easier than using the concept of force since energy is not a vector, and you don’t need to worry about direction. One of the most valuable tools to determine motion is the Law of Conservation of Energy, which states that in a closed system,the total energy of the system stays constant. This means if you determine the total energy of a system at some point in time, at another point in time, the total energy of the system will be the same. Another way to think about this law is to state that energy cannot be created or destroyed. Energy can change forms or be transferred between objects. The motion illustrated in Figure 2 is an example of how the Law of Conservation of Energy can be applied. The total energy of the cart at top of the hill must equal the total energy of the cart at the bottom of the hill.
Figure 2: The total energy at the top of the hill, the middle of the hill, and the bottom of the hill must all be the same. ࠵?࠵?࠵?࠵?࠵? ࠵?!= ࠵?࠵?࠵?࠵?࠵? ࠵?"࠵?࠵?ℎ!+!"࠵?࠵?!"=࠵?࠵?ℎ"+!"࠵?࠵?""(Equation 3) It is worth noting that the above equation does not take into account friction. If friction is a significant factor in the system, then the thermal energy (heat generated by friction) must also be added to the equation. Figure 3: Experimental setup with two tracks.
Part I: Top and bottom of the inclined trackFor this part, you will start the cart at a designated height and let it roll all the way to the bottom of the inclined track. Procedure: 1.Determine the mass of the cart and record this value. 2.For this setup you need two tracks. Attach the first track to a stand so that it makes a ramp. Connect the second track to the first so that it lays flat on the table. Make sure the rails on the tracks match because one of them may be slightly wider than the other. (Figure 3) 3.Level the second track. Put the cart on the second track. If the cart moves, one way or the other, use the leveling screw under the fixed end stop to level the track. 4.Turn on the smart cart by pressing the black button on its side. 5.Click on hardware setup, find the cart listed under “Available Wireless Devices,” and connect it by clicking on the cart number that matches the cart on your table. (Make sure the number on the screen matches the number on the cart.) 6.Make sure that the data is being recorded properly. 7.Using a ruler, find the point on the inclined track which is 10 cm higher than the level track. Place the cart on the inclined track so that the center of the cart is directly over the designated spot. 8.Click on the record button to start recording. Release the cart. (Be careful to not give the cart a push.) Stop the cart once it has reached the end of the level track. 9.Examine the data collected on the computer. Find the maximum value of the velocity listed. This will be the velocity of the cart at the bottom of the ramp. The velocity will begin to decrease after that point due to friction with the level track. Record this maximum velocity in Table 1. 10.Bring the cart to the same height and repeat steps 7 - 9 two more times. Have your instructor check your data before you proceed the next step __________(initials)
11.Find the point on the inclined track that is 5 cm higher than the level track. Place the cart on the inclined track so that the center of the cart is directly over this designated spot. 12.Repeat the previous procedure to collect three sets of data for this new starting height. Record the data in Table 2. Calculations: Show a sample of your work in the space below each data table. 1.For each of the six trials, calculate the potential energy at the staring position of the cart using Equation 2. 2.For each of the six trials, calculate the kinetic energy at the bottom of the ramp using Equation 1. 3.For each of the six trials, calculate the total energy at the starting point of the cart and the total energy at the bottom of the ramp. 4.For each of the six trials, calculate the percent difference between total energy at the starting point of the cart and at the bottom of the ramp. % ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? = 8࠵?࠵?࠵?࠵?࠵? ࠵?#$%− ࠵?࠵?࠵?࠵?࠵? ࠵?&$##$’12<࠵?࠵?࠵?࠵?࠵? ࠵?#$%+ ࠵?࠵?࠵?࠵?࠵? ࠵?&$##$’=8 ࠵?100%In-class questions: 1.Comparing data tables 1 and 2: As you decreased the cart’s starting height, did the total starting energy of the cart increase, decrease or stay the same? Why? 2.Comparing data tables 1 and 2: As you decreased the cart’s starting height, did the final speed of the cart at the bottom of the ramp increase, decrease or stay the same? Explain this result in terms of conservation of energy. 3.Do your results for Part 1 support the Law of Conservation of Energy? Explain any discrepancies.
Part II: Top and middle of the inclined trackFor this part, you will start the cart at a designated height and then stop it about halfway down the ramp. Procedure: 1.Find the point on the inclined track which is 20 cm higher than the level track. Place the cart on the inclined track so that the center of the cart is directly over the designated spot. 2.Use your hand to create a barricade to stop the cart when it is approximately half way down the inclined track (~10 cm mark). 3.Click on the record button to start recording on Page 2 of the program. Release the cart. DO NOT MOVE YOUR HAND. 4.Carefully measure the height of the inclined track at the point where the CENTER of the cart sits at rest against your hand. Record this height (vertical distance between the level track and the inclined track where the cart stopped) in Table 3. 5.Examine the data collected on the computer. Find the maximum value of the velocity listed. This will be the velocity of the cart just before you stopped it with your hand. The velocity may become negative after that point if the cart bounced backward. Record this maximum velocity in Table 3. 6.Bring the cart to the same height and repeat the procedure two more times. Be sure to remeasure the final height of the cart for each run as it may vary depending on the consistency of your hand placement. Have your instructor check your data before you proceed to next part __________(initials) 7.Repeat steps 1-6, starting the cart at 20 cm and stopping at the 5 cm mark. Collect three sets of data for this height combination. Record the data in Table 4. Calculations: Show a sample of your work in the space below each data table. 1.For each of the six trials, calculate the potential energy at the staring position of the cart using Equation 2.
2.For each of the six trials, calculate the potential energy at the point on the inclined track where the cart was stopped. 3.For each of the six trials, calculate the kinetic energy at the point on the inclined track where the cart was stopped using Equation 1. 4.For each of the six trials, calculate the total energy at the starting point of the cart and the total energy at the location where the cart was stopped. 5.For each of the six trials, calculate the percent difference between total energy at the starting point of the cart and at the location where the cart was stopped. In-class questions: 1.Do your results for Part 2 support the Law of Conservation of Energy? Explain any discrepancies. 2.Based on your calculations in this part of the lab, is it appropriate to write the Law of Conservation of Energy as PE = KE? Explain. Part III:Challenge1.Start with the cart in the middle of the level track. Make sure it is not moving. 2.Click on the record button to start recording. 3.Use your hand to give a quick shove to the cart so that it has an initial velocity. You want to push hard enough so that the cart travels a significant distance up the inclined track, but you do not want it to fly off the top of the track. J4.Catch the cart when it reaches its maximum height on the track. (Do not let it slide backward.) Carefully measure the height of the inclined track at the point where the CENTER of the cart has come to rest. 5.Use the Law of Conservation of Energy to calculate the initial velocity of the cart after you pushed it. Show your work in the space below. 6.Now find the maximum velocity indicated on the data table on the computer. Calculate the % error between your calculated velocity and the velocity read by the computer sensor
CALCULATIONS: Homework questions:1.Was your calculated value for this lab’s challenge within 10% of the measured value? What are two possible sources of error? 2.A water skier lets go of the tow rope upon leaving the end of a jump ramp at a speed of 14.0 m/s. As the drawing indicates, the skier has a speed of 13.0 m/s at the highest point of the jump. Ignoring air resistance, determine the skier’s height above the top of the ramp at the highest point.
Data Tables:Mass of cart: ______________________ Height of level track: _____________________ Table 1: Initial height = 10 cm, cart rolls to the bottom of the ramp h ( ) v ( ) PE ( ) KE ( ) Etot( ) Trial 1 Top of ramp 0 0 Bottom of ramp 0 0 Trial 2 Top of ramp Bottom of ramp Trial 3 Top of ramp Bottom of ramp CALCULATIONS: % Difference Trial 1 Trial 2 Trial 3
Table 2: Initial height = 5 cm, cart rolls to the bottom of the ramp h ( ) v ( ) PE ( ) KE ( ) Etot( ) Trial 1 Top of ramp 0 0 Bottom of ramp 0 0 Trial 2 Top of ramp Bottom of ramp Trial 3 Top of ramp Bottom of ramp CALCULATIONS: % Difference Trial 1 Trial 2 Trial 3
Table 3: Initial height = 20 cm, cart is stopped ~1/2 way down the ramp h ( ) v ( ) PE ( ) KE ( ) Etot( ) Trial 1 Top of ramp 0 0 Bottom of ramp Trial 2 Top of ramp Bottom of ramp Top of ramp Bottom of ramp CALCULATIONS: % Difference Trial 1 Trial 2 Trial 3
Table 4: Initial height = 20 cm, cart is stopped ~3/4 of way down the ramp h ( ) v ( ) PE ( ) KE ( ) Etot( ) Trial 1 Top of ramp 0 0 Bottom of ramp Trial 2 Top of ramp Bottom of ramp Trial 3 Top of ramp Bottom of ramp CALCULATIONS: Please have the instructor sign here before you leave the lab. This confirms that you have completed the in-lab portion of the lab report. _________________________________ Instructor’s Final approval / Date % Difference Trial 1 Trial 2 Trial 3