Lab07-ExploringMechanicalEnergy-InPerson-all

pdf

School

University of Florida *

*We aren’t endorsed by this school

Course

112

Subject

Physics

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by ProfessorFlamingo3619

Lab 7: Analyzing Mechanical Energy Physics 112 Lab Group Names: Adapted from Real-Time Physics, Wiley, 2004 In order to understand the equivalence of mass and energy, we must go back to two conservation principles which . . . held a high place in pre-relativity physics. These were the principle of the conservation of energy and the principle of the conservation of mass. — Albert Einstein I. INTRODUCTION The kinetic energy associated with the motion of a rigid object is defined as: where m is the mass of the object, and v is its speed. In this lab we will consider other forms of energy associated with gravitational forces. Suppose you lift an object steadily at a slow constant velocity near the surface of the Earth so that you can ignore any change in kinetic energy. You must do work (apply a force over a distance) to lift the object because you are pulling it away from the Earth. The lifted object now has the potential to fall back to its original height, gaining kinetic energy as it falls. Thus, if you let the object go, it will gain kinetic energy as it falls toward the Earth. It is very useful to define the gravitational potential energy of an object at height y (relative to a height y = 0) as the amount of work done against the gravitational force to lift it through the distance y : U = mgy where m is the mass of the object and g = 9.8 m/s 2 is the gravitational field strength on the surface of the Earth. If we use this definition, then the potential energy of an object is a maximum when it is at its highest point. If we let it fall, then the potential energy becomes smaller and smaller as it falls toward the Earth while the kinetic energy increases as it falls. We can now think of kinetic and potential energy to be two different forms of mechanical energy. We define the mechanical energy as the sum of these two energies: E = K + U

Lab 7: Analyzing Mechanical Energy Physics 112 Copywrite SFSU 2022 2 In this lab you will begin by exploring the common definition of gravitational potential energy to see if it makes sense. You will then measure the mechanical energy, defined as the sum of gravitational potential energy and kinetic energy, to see if it is conserved when the gravitational force is the only force acting. EQUIPMENT This lab uses motion sensors, which measure position and velocity. Generally, you will need to: • Launch the capstone software • Connect the motion sensor or cart and make sure capstone “sees” it • Choose the appropriate pre-formatted experiment file on the desktop as directed in each section below Consult your instructor if you have difficulties. II. GRAVITATIONAL POTENTIAL ENERGY: LIFTING A BALL Suppose that an object of mass m is lifted slowly through a distance y . To cause the object to move upward at a constant velocity, you will need to apply a constant force upward just equal to the gravitational force, which is downward. Question: Which equation describes the amount of energy will you need to lift an object of mass m through a distance y on Earth? Use this equation to calculate the potential energy of a ball of mass 0.5 kg at various distances in the table below: Distance (y) Potential Energy (U) 0.0 m 0.5 m 1.0 m Test your predictions: To test your predictions, obtain a basketball

Lab 7: Analyzing Mechanical Energy Physics 112 Copywrite SFSU 2022 3 1. Set up the motion detector on the floor inside the protective box. 2. Open the experiment file called Measuring Grav Pot E 3. Gravitational Potential Energy ( U ) will be calculated from mass times gravitational acceleration ( g ) times the position measured by the motion detector. Then gravitational potential energy will be graphed in real time. 4. Set the motion sensor data collection frequency to 100 Hz in Capstone. Set the motion sensor switch to wide beam on the physical motion sensor (might look like a wide radar beam, or look like a person, depending on your motion sensor). 5. Hold the ball from the sides or above with your hands. Starting with the ball slightly above the motion detector ( keeping your hands and body out of the way of the motion detector ), begin graphing position and gravitational potential energy as you raise the ball to about 1.5 m above the motion detector. Be sure that the ball remains directly above the motion detector. 6. Sketch your results on the axes below. Question 1-2: Do the two graphs look similar? Does this surprise you? Explain. Question 1-3: Gravitational potential energy is always measured with respect to a particular height where its value is defined to be zero. In this case what has been chosen as this reference level? In other words, for what location of the ball would its gravitational potential energy be zero?

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Lab 7: Analyzing Mechanical Energy Physics 112 Copywrite SFSU 2022 4 III. POTENTIAL, KINETIC, AND MECHANICAL ENERGY: DROPPING A BALL Question: Suppose that the ball is dropped and you know its velocity at a certain time. What equation would you use to calculate the kinetic energy of the ball? Question: Suppose that the ball is dropped from some height. What equation would you use to calculate the mechanical energy (the sum of the gravitational potential energy and the kinetic energy)? Prediction: As the ball falls, how will the kinetic energy change with time ? How will the gravitational potential energy change with time ? How will the mechanical energy change with time ? Prediction: As the ball falls, how will the kinetic energy change with position ? How will the gravitational potential energy change with position ? How will the mechanical energy change with position ? Test your predictions: We can check the predictions by measuring the two types of mechanical energy and their sum as the ball falls. 1. Open the experiment file called Mech Energy . The first tab will display position vs. time and velocity vs. time. The second tab will display U , K , and mechanical energy ( E ) vs. time. The second tab will display U, K , and E vs. position. The mechanical energy is calculated as E = U + K. When switching tabs, you might need to need click on each y-axis and then select the data you want to plot. Contact your instructor for help. 2. You are now ready to examine how gravitational potential energy, kinetic energy, and mechanical energy vary as the ball drops. Hold the ball about 1.5 m directly above the motion detector. Be sure that it will fall on a straight path directly toward the motion

Lab 7: Analyzing Mechanical Energy Physics 112 Copywrite SFSU 2022 5 detector. 3. Begin graphing. Release the ball. Be sure that your body and hands are out of the path of the motion detector after the ball is released. Try to stop the data collection when the ball is about half way down. 4. Sketch your results for each type of energy vs. time and vs. position on the axes below. . 5. Label the interval during which the ball was falling by notating the beginning and end of its motion. Question: How did the variation of kinetic energy and gravitational potential energy compare to your predictions? Question: What seems to be true about the mechanical energy defined as the sum of the kinetic energy and the gravitational potential energy? Did this agree with your prediction? Potential Energy (J) Kinetic Energy (J) Total Energy (J) Time (s) Potential Energy (J) Kinetic Energy (J) Total Energy (J) Position (m)

Lab 7: Analyzing Mechanical Energy Physics 112 Copywrite SFSU 2022 6 IV. POTENTIAL, KINETIC, AND MECHANICAL ENERGY: CART ROLLING DOWN AN INCLINED RAMP Another system where the gravitational force is essentially the only net force is a cart with very small friction moving on an inclined ramp. You can investigate the mechanical energy for this system as the cart rolls down the ramp. In addition to the equipment you have been using, you will need the following: • Cart with onboard motion sensor • Ramp • Protractor 1. Set up the ramp and motion detector as shown below. The ramp should be inclined at an angle of about 5° above the horizontal. Question: The gravitational potential energy of the cart which has traveled a distance x up the ramp is mgy, where y is the height of the cart above the table top. You should be able to find an equation for U in terms of the position x measured by the motion detector along the ramp . ( Hint: y = x sin  .) What is the reference height for the potential energy, i.e., the height where potential energy is zero? 2. Open the experiment file called Inclined Ramp. The three data collection tabs will be the same as in the previous experiment. 3. The mass of the cart and the angle of the ramp have been entered into formulae that will automatically compute the potential, kinetic, and mechanical energy. Prediction: As the cart rolls down the ramp, how will the kinetic energy change? How will the gravitational potential energy change? How will the mechanical energy change?

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Lab 7: Analyzing Mechanical Energy Physics 112 Copywrite SFSU 2022 7 Test your predictions: 4. Hold the cart at the top of the ramp. Be sure that the x-arrow marked on the cart is pointing toward the top of the ramp. Begin data collection . Release the cart. Stop the data collection before the cart reaches the bottom of the ramp. 5. Sketch your graphs on the energy vs. position axes below. Question: Compare your graphs to those for the falling ball in Section III. How are they similar and how are they different? Question: What kind of variation, if any, is there in the mechanical energy as the cart rolls down the ramp? Does this agree with your prediction? Explain. Potential Energy (J) Kinetic Energy (J) Total Energy (J) Position (m)

Lab 7: Analyzing Mechanical Energy Physics 112 Copywrite SFSU 2022 8 V. POTENTIAL, KINETIC, AND MECHANICAL ENERGY: CART ROLLING UP AND DOWN AN INCLINED RAMP Prediction: Suppose that the cart is given a push up the ramp and released. It moves up, reverses direction, and comes back down again. How will the kinetic energy change? How will the gravitational potential energy change? How will the mechanical energy change? Describe in words and sketch your predictions with labeled dashed lines on the axes below. Test your predictions: 6. Give the cart a push up the ramp, starting from the bottom of the ramp. Start the data collection immediately after letting go of the cart. Stop the data collection just before the cart reaches the bottom of the ramp on the way back down. Prediction Observation Question: How does the mechanical energy change as the cart rolls up and down the ramp? Does this agree with your prediction? Explain. Potential Energy (J) Kinetic Energy (J) Total Energy (J) Position (m) Potential Energy (J) Kinetic Energy (J) Total Energy (J) Position (m)

Lab 7: Analyzing Mechanical Energy Physics 112 Copywrite SFSU 2022 9 Post-Lab Knowledge Check A ball is tossed in the air and released. It moves up, reverses direction, falls back down again, and is caught at the same height it was released. a. Considering the interval after the ball is released and before it is caught, when does the gravitational potential energy of the ball have its maximum value? Minimum value? Explain. b. When does the kinetic energy of the ball have its maximum value? Minimum value? Explain. c. What about the total energy of the ball? What can you say about its value at the locations described in your answers to (a) and (b)? d. Draw graphs of potential energy, kinetic energy, and total energy as a function of position .

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Lab 7: Analyzing Mechanical Energy Physics 112 Copywrite SFSU 2022 10 Summary (Look at your lab notes while doing this!) 1. Write down one major conclusion you can draw from this week’s laboratory. Please explain in detail . 2. Describe the experimental evidence that supports your conclusion. Please explain in detail . 3. Give one example of applications/situations for the finding(s) you described above in your (everyday) life outside of physics lab, and explain the connection.

Lab07-ExploringMechanicalEnergy-InPerson-all

Related Documents