Ishmam Zaman- Smart Cart - Work and Kinetic Energy

pdf

School

Sacramento City College *

*We aren’t endorsed by this school

Course

410

Subject

Mechanical Engineering

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by BailiffFang8404

/ we Liliern AT ... R, e, J/12047.._.. SMART CART — WORK AND KINETIC ENERGY Driving Question | Objective How is the work done on an object by a force related to the change in that object's kinetic energy? Investigate the relationship between the change in kinetic energy of an object experiencing a non- zero net force, and the work done by that net force on the object. Establish a measurement-based relationship between work and kinetic energy. Materials and Equipment o PASCO Smart Cart with hook accessory ¢ Hanging mass, 100-g o PASCO Cart Masses, 250-g (4) o Thread o PASCO Dynamics Track with feet * Balance, 0.1-g resolution, 2,000-g capacity « PASCO Super Pulley with Clamp (1 per class) Background WoORK The work W done on an object by a constant force Fis dependent on the magnitude and direction of the force, as well as the magnitude of the object’s displacement (distance) d. When the force is parallel to the object’s displacement, the expression for work done by the applied constant force simplifies to: W =Fd [¢))] When the magnitude of the applied force is variable, the mathematical expression for work done by the force grows more complicated, but can be simplified as the area under a force versus position curve: Wariable torce = Area Under Force vs. Position Curve @ In this investigation you will use this graphical relationship to determine the work done on a cart by constant and variable forces. KINETIC ENERGY An object's kinetic energy K is described by the equation: K= %mu’I 3) where m is the mass of the object and v is the object's speed. Although work and kinetic energy are different quantities, they are closely related to each other in a mechanical system. Collect data using the following procedure, and then use that data to investigate the relationship between the change in kinetic energy of a cart and the work done on the cart by constant and variable forces. RELEVANT EQUATIONS Wioaciabie o = Area Under Force vs. Position Curve 0]

SMART CART - SMART CART — WORK AND KINETIC ENERGY Procedure Part 1- Constant Force SeTUp 1. Set up the equipment like the picture below. NOTE: Make certain the pulley is hanging over the edge of the table, and the track is as level as Ppossible. Adjust the height of the pulley so that the thread between the cart and the pulley is parallel with the surface of the track. 2. Open the experiment file SC Work & Kinetic Energy, and then power-on the Smart Cart and connect it wirelessly to your software. 8. In the experiment file is a graph of force and speed versus position. The hook on the front of the smart cart will measure the force applied by the tension in the string, while the cart’s wheels measure its speed and position. CoLLECT DATA 4. Unhook the thread from the cart, and then measure the mass of the cart plus the four 250-g cart masses. Record this value above Table 1 in the Data Analysis section below. 5. Set the cart on the track, and then zero the cart’s force sensor in your software before re-hooking the thread to the cart. 6. Re-attach the thread to the hook on the cart, and then roll the cart all the way to the end of the track opposite the pulley (or as far back as you can without the hanging mass touching the pulley) and hold it in place. 7. Wait for the hanging mass to stop swinging, and then start recording data. 8. Release the cart to roll freely down the track, and then catch the cart before it rolls into the pulley. Data recording stops automatically after 1.5 seconds. 9. Use the tools in your software to determine the area under your force versus position data, and the final speed of the cart at the last position data point. Record the area and speed values in Table 1. PASCO

SMART CART - SMART CART - WORK AND KINETIC ENERGY Part 2 - Variable Force CoLLECT DATA 10. Unhook the hanging mass from thread. 11. Set the cart at the end of the track opposite the pulley so it rests in place. Have a group member hold the loose end of the thread in their hand at the other end of the track (no tension in the thread). 12. Start recording data, and then gently pull on the string so the cart rolls down to the other end of the track. Catch the cart before it rolls into the pulley. Data recording stops automatically after 1.5 seconds. NOTE: The force that you apply to the string does not need to be so soft that the cart barely rolls; but don’t pull the thread so hard that the cart rolls into the pulley and off the end of the track. 13. Use the tools in your software to determine the area under your new force versus position data, and the final speed of the cart at the last position data point. Record the area and speed values in Table 1. Data Analysis Mass of cart and cart masses (kg) = O 7 g 7 b’ Kﬂ Table 1: Work and energy data for a cart experiencing a constant applied force Part Work = Area Under Fvs x Final Speed Change in Kinetic Energy (N-m) (mls) ) T | 004 Nem@ 0.g1 1 /g | 04301 o 030 e @] 0,610 Ml | 04yL 14. Use your speed data, the mass of the cart and cart masses, and equation 3 to calculate the change in the cart’s kinetic energy in parts 1 and 2. Assume that the cart’s initial kinetic energy 3 was zero in both parts. Record your results in Table 1. AK=Keg—K Ko=0 k:]T—MV1 aKy = 5 (0.7571 k) (0.41] 'v/s)L= 0.30] J AKy =L (0,757‘1:<9)(0,é12 m%)z: 0.142

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

SMART CART - SMART Analysis Questions. © 1. How does the work done on the cart compare to the object’s change in kinetic energy for each part? The ok dore %Lu/ﬂ( ; M/ v T sate 2 2K malot, 2 The ek At s sligZgy, hiphn © 2. How do the units for the area under your Force versus Position curve (work) compare to the units associated with change in kinetic energy? v L NeM= K9 Mje = K9 " J=k9- "/, e fhewn e undly ¢p ok done iy Lo gome ar choga KE © 3. Imagine you had performed a third trial in which you had pushed the cart from behind rather than pull it by the thread. If the cart started from rest, and the total work done by the pushing force to move the cart was 0.5 J, what would be the cart’s change in kinetic energy? Use your data to justify your answer. MAKEM/& Wfi%e WM, © 4. Inone sentence, describe what you believe the mathematical relationship is between the work done by a non-zero net force on an object, and the change in that object’s kinetic energy. Be specific, and use terms like “proportional to,” “equal to,” “inversely proportional to,” and so on. %MMMMW»ZWMWM an WW’#W/@MMW% Yy, 7