Impulse word thermodynaics

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Jan 9, 2024

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Lab 2.3 Impulse, Work, and Thermodynamics Introduction Watch the video on the Assignment page. When the fire extinguisher pushes the man on the skateboard, he gains both momentum and kinetic energy. By knowing how much force is applied to him for how long and over what distance, we can calculate his eventual momentum and kinetic energy. Formulas I = Impulse = (Avg. Force) (Time applied) = Ft Impulse = Change in Momentum = (Final Momentum) – (Initial Momentum) For measuring the velocity: v = d/t Work = (Avg. Force) (Distance moved) = Change in Kinetic Energy The conservation of energy, when extended to thermodynamics predicts that as work is done on a substance, heat energy will transfer to the object’s internal energy, causing a predictable rise in temperature. Formula Heat = ( Specific Heat Capacity ) ( Mass ) ( Change ∈ Temperature ) = Q = Cm∆T ∆T = T final − T initial Part 1: Impulse and Change in Momentum We’ll start with the Physics Aviary Simulation Impulse Lab A data table is provided for recording all your data and results of your calculations.  Open the simulation and click “Begin.”  Adjust Wally’s Mass and the Extinguisher’s Force to change them from the default values.  Adjust your mass value to something between 42 kg to 90 kg. Instructor will use 35 kg.  Adjust your force value to something between 50 N and 190 N. Instructor will use 200 N.  Adjust the Maximum Speed and Maximum Momentum settings to the highest available (40 m/s and 4000).  Click Activate and watch Wally accelerate, gaining momentum as he moves.  Click Shut Off before Wally reaches the red lines at the left (about when he is above the word “Time”).  Wait for Wally to pass through the photogates (red lines at left). These allow you to measure the final velocity, which is used to calculate the momentum.  Since there is no net force on Wally after shutting off the extinguisher exhaust, Wally should be moving at a constant velocity, as required by Newton’s First Law. 1

Make a screenshot of your simulation after Wally has passed through the photogates. Record the data listed in the table below. Quantity Measurement Unit Mass 85 kg Force 100 N Both times are given in ms (milliseconds). Convert to seconds by dividing each number by 1000. Record the times in seconds in the spaces below. Time the extinguisher was firing 9468 ms Photogate time 884 ms Use these data to calculate the following quantities, putting your measurement values and units for the appropriate variables in the formulas where there are pairs of parentheses and calculate the result. Keep 2 digits after the decimal point. If you don’t show the values in the “Your Substitutions” section, your results grade will be 65%. If you show substitutions without units, your results grade will be 75%. If you copy the instructor’s demonstration data, you will get 50% credit only. Formula Your substitutions Your result Units Impulse: I = F t (100 N) (9.468 s) 946.8 N * s For t, use the Time the extinguisher was firing, in units of seconds. Final velocity: v = d/t (10 m) / (0.884 s) 11.31 m/s For t, use the photogate time, in units of seconds. Final Momentum: p = mv (85 kg) ( 0.01 m/ms) 8500 Kg*m/ms Since the starting velocity was zero, this should also be the change in momentum, which should be equal the impulse, according to Newton’s Laws. 2

There is another way to estimate the final velocity: Divide the Impulse by the mass. v = Impulse/mass (946.8 N *s) / (85 kg) 11.14 N*s/kg This should be close to the velocity calculated in the 2 nd calculation above. The simulation provides an additional data field for Momentum Gained. Experience shows this value rarely matches the measured value so do not worry if this field does not match your results closely. Impulse should equal change in momentum to within about 5% error. Problem 3 of the PHY120 Unit 2 Practice Problems is similar to this simulation. Example: An adult helping her child learn to ride a bike, applies a net force of 4.86 newtons to the child on the bike for 5.61 seconds. How much momentum does the child and his bike gain after being pushed by the adult in kilogram-meters per second? Round your final answer to two decimal places. Since you don’t know the mass of the child and bike or the change in velocity, you cannot calculate the momentum gain using the formula for momentum. You have to calculate the impulse: ∆ p = I = Ft = ( 4.86 N ) ( 5.61 s ) = 27.26 Ns = 27.26 kg m s Part 2: Work and Change in Kinetic Energy Open Kinetic Energy Lab . This operates much like the previous lab, but we will be observing the relationship between work done and kinetic energy gained. Instead of measuring the time the force is applied, you will measure the distance Wally moves while the force is applied. Use the same values for Force and Mass as you used in Part 1. Increase the Maximum Speed setting to 40 m/s and the Maximum Energy to 20,000 J. As before, click Activate to start the experiment. Click Shut Off before Wally gets to the red lines. Shut off when Wally is between 50 to 60 meters from the start. Make a screen shot of your results. 3

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Measure distance to the left side of Wally’s Life Support backpack. Estimate to the nearest meter. Quantity Measurement Unit Mass 85 kg Force 100 N Distance while extinguisher was on 56.5 m Photogate time (convert ms to s as before) 0.840 s Round each result to two decimal places, but don’t round the speed when substituting into the kinetic energy formula. See instructions on the substitutions grade in part 1. Formula Your substitutions Your result Units Work = Force x distance = F d (100 N) (56.5 m) 5650 N* m For d , use the distance the fire extinguisher was applying a force. Final speed: v = d/t (10 m) / (0.840 s) 11.9048 m/s For t, use the photogate time, in units of seconds. Keep at least 4 decimal places in this result to avoid round-off error when substituted into the next equation. Final Kinetic energy: KE = (1/2)mv 2 (0.5)(85kg) (11.9048) 2 6023.28 Kg * m/s This should equal (approximately) the Work done. The simulation provides an amount of Energy Gained. Experience shows this does not closely match the work done or the kinetic energy gained, so do not worry if this value is not exactly the same as your results. Tests show the difference between work done and KE gained (as calculated with the mass and velocity measurements) should be to within about 10% error. Don’t worry if your work and kinetic energy values are not so close. 4

Part 3: Mechanical Equivalent of Heat Lab Open the simulation: https://www.thephysicsaviary.com/Physics/Programs/Labs/MechanicalEquivalentOfHeatLab/ See Canvas for the link Mechanical Equivalent of Heat Simulation . Observe how the simulation works as the instructor demonstrates. Make sure your simulation window is maximized so it will be big enough read the amounts for mass and volume when you make screen shots. Make a screenshot of the simulation before running the experiment and paste it below. Then run the experiment and paste a screenshot of the result. Make sure the falling weight reaches the ground before using the Snipping Tool to make a screen shot. Screen shot should fill the page from left to right. Image of Simulation Before running the experiment: Note: do NOT click on the grey cylinder weight at the right between taking screen shot 1 and 2. Image of Simulation After running the experiment: 5

Save your document to preserve your initial and final conditions. Complete the following data tables, multiple choice questions, and calculations. For entering your temperature unit, copy and paste °C. Data and calculations Value Units Volume of water in container 285 mL Convert this to mass in grams, 1 mL has mass of 1 gram Mass of water 285 g Mass of cylinder on right 265000 g Height of cylinder 4 m Temperature of water, initial 8.70 C Temperature of water, final 16.60 C After observing a simulation run, answer the following questions: Does the weight accelerate as it falls or fall at a constant velocity? a The weight accelerates X b The weight drops at a constant speed Focus on the mechanical energy of the system. As the weight drops, it is X a Gaining kinetic energy and losing an equal amount of potential energy b Losing kinetic energy and gaining an equal amount of potential energy c Gaining potential energy and losing an equal amount of kinetic energy d Losing potential energy and not gaining any kinetic energy Make sure the question is not split between two pages. Add space if necessary. As the weight falls, it loses mechanical energy. Where is that energy going? X a The weight is gaining an equal amount of kinetic energy. b The weight is gaining internal energy (its temperature goes up) c The water is gaining internal energy due to the paddles. 6

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Calculate the weight of the object on the right. Weight = mass x gravity = 285 × 9.80 N kg = ¿ 2793 g * l/k weight x loss of height= Loss of potential energy Substitute values: This should equal the heat that went into the water, which will be calculated next. ∆Temperature = ¿ T final − T initial = ¿ 7.9 C Heat = mass×specific heat capacity ×∆T = C m ∆T For mass, use the mass of the water in grams. For the specific heat capacity, use 4.186 J g ℃ . Show substitution: HEAT = (285) (4.186) (7.9) Heat= 9424.78 The heat gained by the water should approximately equal the mechanical energy lost by the falling weight. Part 4: Electrical Equivalent of Heat Open the Electrical Equivalent of Heat Lab in Physics Aviary. Click “Begin”. For this experiment, we have an electrical device that runs current through a resistor located in a container of water. As current runs through the resistor, electrical energy is converted into heat, which raises the internal energy of the water and increases the water’s temperature according to the formula used in the previous part: Q = m C ΔT In this experiment, we’ll use a formula to be explained later to calculate the heat added. We’ll use that heat, the mass, and change in temperature to calculate the specific heat capacity of the liquid (water). All the values measured in this lab are randomly set each time the lab begins. Be careful not to click anywhere except the power switch during the experiment or you might change one of the measurements mid-experiment, which would invalidate your results.  Fill in the table below with the volume of the water, listed just above the container with the water.  As before, the volume in milliliters ( ml ) will also equal the mass of the water in grams. 7

 Also record the initial temperature. Since the temperature meter fluctuates, pick a value between the high and low temperature observed. Round the average initial temperature to the nearest tenth of a degree C . The temperature unit should have the degree symbol: º in front of it. Copy this symbol in the above sentence and paste it with the Celsius temperature abbreviation, º C . IMPORTANT: read all instructions before starting. The screen shot has to be made while the current is running.  Click on the power switch at the lower left of the simulation display. The voltage, current meter, and timer should display the relevant measurements to calculate the heat added to the system.  Let the current run and observe that the temperature is increasing.  Once the current is flowing , make a screen shot of the simulation and paste it below.  Record the voltage and current values. You will learn more about these quantities in Unit 4 Class 1.  Wait until the timer exceeds 120 s or the temperature exceeds 80 ºC, whichever comes first. Then stop the experiment by clicking on the power switch again.  Record the final temperature (average value as before).  Record the time.  Calculate the heat, change in temperature, and specific heat capacity. 8

 While showing your substituted values is not required in this part of the lab, it is always recommended that you write the equation and then write the values from your data into the equation, with units, and then calculate your answer. You can do this in your notebook. Experience has showed it helps you remember all the key steps and will allow you to catch errors if you make any. Table begins on next page. 9

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Quantity Measurement Unit Water volume 306 ml Water mass 306 g Initial temperature (avg) 11.3 C Voltage 87 V Current 4.9 A Final temperature (avg) 48.4 C Time 120 s Formula for Heat: (Voltage)(Current)(time) Heat (round to nearest whole number) 51156 Measured Change in Temperature Formula for Specific Heat Capacity C = ( Heat ) [ ( m ) ( ∆T ) ] Calculated Specific Heat Capacity of water (round to 3 places after the decimal) Correct Specific Heat Capacity of water 4.186 J/(g ºC) Calculations: Electrical Power = (Voltage in Volts, V )(Current, in Amperes, A ) Answer unit is standard power unit: Watts, W . When you multiply the power times the time in seconds, you get the energy used in Joules. This is heat added to the water. Heat ( Q ) = (Power in Watts, W )(Time in seconds, s ) Answer unit is standard energy unit: Joule, J Variables: Q stands for heat. V stands for Voltage. I stands for Current. t stands for time. Once you know the heat, mass, and change in temperature, we can calculate the specific heat capacity. We start with the equation used earlier. Heat = mass ×specificheat capacity ×∆T Q = m C ΔT Solving this equation for C we get 10

C = Q ( m ∆T ) C = ❑ ()() The measured change in temperature = (Final T) – (Initial T) The calculated specific heat capacity and the standard value should be within 2% difference. Remember that because of the uncertainty of the temperature measurement, the actual measured change in temperature could be off by as much as 0.6 ºC. There is also a lot of uncertainty introduced by the current meter, which is only accurate to the nearest tenth of a unit. A slight error in reading the current can translate into a considerably different heat calculation, which then carries through to the specific heat capacity value. Make all measurements as accurately as you can. 11