Phys Lab3 - MotionDownandBackUpandInclinedPlane...

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Motion Down and Back Up and Inclined Plane John Domanick 10/5/10 Partner: Matt Weiner Teaching Fellow: Tim Harden
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Abstract: In this experiment we investigated the motion of a glider on an inclined air track. By observing the motion down and up the track we aimed to calculate both the coefficient of kinetic friction between the glider and track, μ , and the angle of inclination of the track, θ . By measuring the position of the glider as a function of time, we were also able to find the velocity and acceleration/time functions. We found that the acceleration was constant through the glider’s path, which is reasonable as the forces acting on the glider; gravity, friction and the normal force are all constant. Through this experiment we found that that coefficient of kinetic friction between the glider and the track was 3.38x10 ‐4 ± 4.62x10 ‐4 . We also calculated the angle of inclination of the plane to be 1.63 o ± 0.04 o , and measured it with an inclinometer to be 1.6 o ± 0.1 o .
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Theory: A body moving up or down an inclined plane is under the influence of three constant forces: gravity, friction, and the normal force exerted by the plane. Due to the forces affecting the body being constant, we also know that its acceleration while on the plane is constant, from Newton’s second law, F=ma. (1) Since the body is accelerating parallel to the plane, we know that the sum of forces perpendicular to the plane is equal to zero. These forces are the normal force, (F N ) and the perpendicular component of gravity, (F gy ). F N + F gy = 0 (2) We can see from the free body diagrams that, F gy = F g cos θ = mg cos (3) where m is the mass of the body, and g is the acceleration due to gravity, and theta is the angle of inclination of the plane. Plugging back into Eq. 2 gives us, F N = F gy = mg cos (4) Also from the free body diagrams we see that the net forces for both the upward and downward movement are: F net ( d ) = F gx F F (5) for the downward motion, and F net ( u ) = F gx + F F (6) for the upward motion, where F gx is the component of the force of gravity parallel to the inclined plane, and F F is the force of friction. The force of friction on any object, on any surface is equal to: F F = μ F N (7) where μ is the coefficient of friction between the object and surface. This is an intrinsic property of both the object and surface, and one of the parameter of inclined plane motion that we will be searching for. Also from the free body diagrams we see that F gx = F g sin = mg sin (8) Now combining Eqs. 1,4 ,7, and 8 and plugging them into 5 and 6, we get F N F F F g F gx F gy v a d Diagram 1 F N F F F g F gx F gy v a u Diagram 2
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F net ( d ) = ma d = mg sin θ μ mg cos (9) F net ( u ) = ma u = mg sin + mg cos (10) Lastly by cancelling m from both sides of these equations we are left with: a d = g sin g cos (11) a u = g sin + g cos (12) We can now use these equations to find both theta and mu from our experiment.
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This note was uploaded on 10/06/2011 for the course PHYS 19 taught by Professor Blocker during the Fall '10 term at Brandeis.

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Phys Lab3 - MotionDownandBackUpandInclinedPlane...

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