Phys 1 Student Workbook.pdf

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Physics Labs with Computers, Vol. 1Student WorkbookP24: Conservation of Linear and Angular Momentum 012-07000APre-Lab For You To DoUse the Photogate/Pulley System to measure the motion of the Rotating Platform and ProjectileCatcher and the ball as the rotating system is pulled by a hanging mass. Use DataStudio orScienceWorkshop to calculate the tangential acceleration. From the results, determine therotational inertia of the rotating system (consisting of the Rotating Platform and ProjectileCatcher with ball).Pre-Lab BackgroundTo find the rotational inertia of the system, apply a known torque to the system and measure theresulting motion.Since τ = Ια, solving for the rotational inertia, I, gives I = τ α .where α is the angular acceleration and τ is the torque. Now, τ = r × F, where r is the distancefrom the center of the rotating system to the point where a force is applied, and F is the appliedforce. In this case, the applied force is the tension (T) in a string that is tied to a step pulley thatis part of the Rotating Platform. A hanging mass m pulls the string. The value of r is the radiusof the step pulley on the platform. The radius is perpendicular to the applied force (T).Therefore, for this activity, the torque is: τ = rT .Applying Newton’s Second Law for the hanging mass, m, results in: ∑ F = ma = mg − TSolving for the tension in the string gives: T = m(g − a). The expression for torquebecomes: τ = rT = rm(g − a)The linear acceleration a of the hanging mass is the tangential acceleration, a T , of the rotatingapparatus.The angular acceleration is related to the tangential acceleration as follows:α = a TrSubstituting for the torque and angular acceleration gives:I = τ α = rm(g − a) ÷ a Tr= rm(g − a) = mgr 2⎛ g ⎞− mr 2 = mr 2 ⎜ − 1⎟r a Ta T ⎝ a T ⎠The rotational inertia, I, can be calculated from the tangential acceleration, a T , the hangingmass, m, and the radius of the step pulley, r.p. 170 ©1999 PASCO scientific P24
Name _____________________ Class ______________ Date _________Pre-Lab PART I: Computer Setup1. Connect the ScienceWorkshop interface to the computer,turn on the interface, and turn on the computer.2. Connect the Photogate’s phone plug to Digital Channel 1on the interface.3. Open the document titled as shown:500 scientificPASCOInterfacescientific300PASCOANALOG CHANNELSScience W orkshop DATA LO G G ING INSTRUCTIONSScienceWorkshopInterfaceDataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win)P24 Prelab Linear Angular.DS X28 Inertia X28_CLAM.SWS• The DataStudio document has a Workbook display. Read the instructions in the Workbook.• The ScienceWorkshop document has a Graph display of Velocity versus Time and a Digitsdisplay of Velocity.• Note: The spoke arc length for the Photogate/Pulley System is set at 0.015 m. If you areusing a different pulley, change the spoke arc length in the sensor window by doubleclicking on the Smart Pulley icon in the Experiment setup window.Pre-Lab PART II: Sensor Calibration and Equipment Setup• You do not need to calibrate the Photogate/Pulley System.1. Put the Rotating Platform on a horizontal surface near the edge of the surface.2. Use a large rubber band to attach the Projectile Catcher to one end of the RotatingPlatform.Projectile Catcher Accessory -side viewRubber bandRubber bandRotating Platform - end viewProjectile Catcher Accessory -end view3. Use the leveling feet to level the platform.4. Place the 1-inch (2.5-cm) steel ball into the catcher. Align the ball with the centerline ofthe platform.5. Put the support post in the base of the Rotating Platform.6. Use the Pulley Mounting Rod to attach the Pulley to the tab onthe Photogate.7. Mount the rod of the Photogate/Pulley System in the hole ofthe support post.8. Use a piece of string that is about 20 centimeters longer than the distance from the top ofthe Photogate/Pulley System to the floor. Tie one end of the string through a hole in thestep pulley that is on the Rotating Platform shaft. Put the string in the groove on the pulley.9. Attach a mass hanger to the other end of the string.P24 ©1999 PASCO scientific p. 171
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