IP - IP Inclined Plane revised ply an additional force to...

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1 Inclined Plane IP Inclined Plane revised July 11, 2005 Learning Objectives: During this lab, you will 1. be introduced to how to write a lab report. 2. learn how to take data with Logger Pro . 3. estimate the uncertainty in a quantity that is calculated from quantities that are uncertain. 4. test a physical law experimentally. A. Introduction You will check the validity of Newton’s Second Law by measuring the motion of a cart as it accelerates up an inclined plane under the action of gravita- tional and other forces. You will use an “encoded pulley” to convert the motion of the cart to an electronic signal that will be monitored by a computer. The computer will use the program Logger Pro to read and dis- play this signal in terms of position, velocity and acceleration as a function of time. You must complete a fill-in-the-blank report for this lab experiment, worth 30 points. Appendix II has details of how to write reports. Appendix XI is a sample report. The fill-in-the-blank report is in Appendix IX. A Word version of the fill-in- the-blank report is available on the web. Additional guidance may be supplied to you in lab. B. Apparatus You will measure the motion of a low- friction PASCO ® cart along its mating track. A ring stand holds the track at a fixed angle while a string, mass holder and masses sup- ply an additional force to balance or acceler- ate the cart. An encoded pulley and a com- puter running the program Logger Pro ® monitor the motion. An electronic scale and meter stick are used for measuring key char- acteristics of the system. C. Theory Newton’s Second Law provides the basic theory for this experiment. The vector form of this law for the motion of a body of constant mass m is Fm a = G G (1) where Σ denotes a sum and F G therefore represents a vector sum of all external forces acting on the body. a G is the acceleration of the body. For motion in two dimensions, this corresponds to two independent equations, Σ F x = ma x and Σ F y = ma y (1a) that is, the vectors can be resolved into com- ponents along two axes. For an inclined plane a natural choice is for the x- direction to be parallel to the plane and the y -direction to be perpendicular to the plane. The forces that act on the cart (which has mass m 2 ) in this experiment while the cart is moving up the inclined plane under the influence of a string and counterweight are illustrated in Figure 1. The gravitational force 2 mg G points directly down towards the center of the earth. The normal force N G is the force on the cart that prevents it from Figure 1: Schematic of Forces in Experiment θ m 2 g f N T 2 m 1 g T 1 y x y x
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Inclined Plane 2 sinking into the metal track. This force points perpendicular to the track. The force of friction f G points along the track, opposite to the direction of motion of the cart. If the pulley is frictionless and massless ( which we will assume is true in this experiment ), the magnitude of the string tension is the same on both sides of the pulley () 12 TTT =≡ GG
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IP - IP Inclined Plane revised ply an additional force to...

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