Copy of Lab 9_ Work Energy Theorem (1)

.pdf

School

San Diego State University *

*We aren’t endorsed by this school

Course

182A

Subject

Physics

Date

Dec 6, 2023

Type

pdf

Pages

Uploaded by SargentOtterPerson3842

PHYSICS 182A/195L LAB REPORT - LAB 9: Work Energy Theorem Lab 9: Work Energy Theorem San Diego State University Department of Physics Physics 182A/195L TA: Alvin Yassuiae Lab partner 1: Anna Wren Vanden Bosch Lab partner 2:Breanne Nicolas Date:10/31/23 Score: Theory Work is the change in energy of a system (one or more objects with mass) as the result of a force applied to that system. How exactly is force related to energy? Let’s think of an example. Recall that if a mass is held at a height h above the earth, then it has a potential energy . In order to move an object from the ground ( ) to a height , then it must have at least force acting on it while it moves from to (otherwise gravity would pull it back down). If we simply replace with in the expression for energy, we get: That is, the potential energy of the object is equal to the force we had to apply to it, times the distance , that it moved while the force was applied. More generally, any constant force applied to an object over some distance will change the energy of that object: This change in energy could be potential energy or kinetic energy, depending on the circumstances. A change in energy of a system due to a force is called Work. 1 Department of Physics

What if the force is not constant? A situation with non-constant force requires calculus. For a force that changes with , the work done by that force is This is one way to write the work-energy theorem , which tells us exactly how to compute the work done on a system by a changing force . Constant force Let’s use the work-energy theorem to calculate the work done on a cart with mass by a constant force. To generate a constant force, we will use a hanging mass attached to the cart with a pulley system. This way, a known hanging mass can be used to calculate the force applied to the system. Note that the force acting on the cart is not , it is the tension in the string. Using the free-body diagram above, and the fact that both masses must have the same acceleration, we can determine that the tension acting on the cart is: (For a detailed derivation, see the appendix.) Therefore, the work done on the cart by the pulley system is : Here, is the distance that the cart has moved. (It is also the distance that the hanging mass has fallen. Why?). Linear force Next, we’ll use the work-energy theorem to calculate the work done on a cart with mass by a linear force . To generate a force which changes linearly with x, we use a simple spring, which obeys Hooke's law:

PHYSICS 182A/195L LAB REPORT - LAB 9: Work Energy Theorem Here, is the spring constant and is the distance the spring is stretched from equilibrium. Suppose that the cart starts from some initial displacement , where the spring is taut. The cart is then released, so that the spring pulls it to the right. The force applied by the spring is changing linearly, since as the cart changes it’s x-position, the length of the spring changes and so does the force it applies. The total work done on the cart by the spring from the carts initial position to its final position is given by the work-energy theorem: This integral can be computed with the power-rule from calculus: An integral of a function is nothing but the area under the curve. Therefore, the work done by the force can also be seen as the area under the curve. In this case, the curve is a linear function with slope . The area is just the area of a triangle with base length and height , so 3 Department of Physics

Procedure Setup 1. Use the Balance Scale to measure the mass of the Smart Cart alone, the Smart Cart + the four 250g Stackable Masses. Record these values in Table A.1. 2. Connect the Wireless Smart Cart via Bluetooth under Hardware Setup in Pasco Capstone TM . 3. Lay the cart flat on the table and make sure only the hook is attached. Go back to hardware setup and click on the smart cart force sensor settings (blue gear). Click “zero sensor now” to zero the force sensor. Part A: Constant Force 1. Set up the equipment as shown in Figure A.1 , but place magnetic End-Stops on both ends of the track. There is a hole in the End-Stop that you can thread the string through during the experiment. Put the 4 stackable 250g masses on the cart. 2. Cut about 1 meter of string. Tie one end of the string to the hook of the cart. Thread the string through the End-Stop and tie the other end to a Mass Hanger. 3. Hang the mass hanger over the pulley and place 45g on the mass hanger. Record the total hanging mass (hanger + weights) in Table A.1. Figure A.1: The cart is placed in the center of a level track, attached to a pulley system . 4. Roll the cart as far back as you can before the mass hanger touches the pulley. Hold it in place. 5. Measure the displacement of the cart from the end of the track (pulley end) using the measuring tape on the track. Record this value in Table A.1. 6. Wait for the hanging mass to stop swinging, then hit START to begin recording. 7. Release the cart to roll freely down the track, and then catch the cart before it rolls into the End-Stops. Hit STOP to stop recording. 8. Use the “Highlight tool” to select only the data points recorded when the cart was in motion, and which have positive force values. 9. Record the area under the Force vs. Position curve. using the “Display Area tool” to calculate the area. Record the value in Table A.2. 10. Determine the average force using the “Mean tool”. Record the value in Table A.2.

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

Recommended textbooks for you

Physics for Scientists and Engineers: Foundations...

Physics

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Cengage Learning

Physics for Scientists and Engineers with Modern ...

Physics

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Cengage Learning

College Physics

Physics

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Cengage Learning

College Physics

Physics

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Cengage Learning

Principles of Physics: A Calculus-Based Text

Physics

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Cengage Learning

Physics for Scientists and Engineers

Physics

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

Recommended textbooks for you

Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning