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Unformatted text preview: Pre-Lab Required Homework Problem Preparation for Experiment 3, Part 1 X78 The figure above shows a block sliding upward on an inclined plane. Assume that at t = 0 the block is at x = x and has a velocity v in the direction of increasing x . The block is acted upon by gravity and by kinetic friction between the block and plane that can be modeled by a coefficient of kinetic friction k . The block reaches a position x = x + D where it stops and then begins to slide back down the plane. The coefficient of friction is assumed to be small, in particular k < v 2 / 4 Dg cos . a) Put the limit on the magnitude of the kinetic friction in context. What physical outcome does this limit assure? b) Find the analytic expression that represents x ( t ) from t = 0 until the time the block reaches the highest point of its travel. During this time components of the gravitational force and the friction force act in the same direction. Find another analytic expression that represents x ( t ) from the top of the blocks travel until the time it reaches the bottom of the plane. During this time components of the gravitational force and the friction force act in opposite directions. Thus the magnitude of the acceleration is different in the two time intervals. c) Make a careful sketch of x ( t ) d 2 x/dt 2 over the entire time interval. Preparation for Experiment 3, Part 2 y x 4.2 cm The above figure represents the configuration of Experiment 3. Note the differences from the situation you analyzed in Part 1. The block has been replaced by a cart with wheels. At the bottom of the track the cart hits a spring rather than falling off the plane. The position x ( t ) is now measured from the top of the plane, that is, largest positive values of x occur when the cart is compressing the spring. The experiment is run by releasing the cart from near the top of the plane and recording its position x ( t ) and the force exerted on it by the spring f ( t ) as the cart descends and rebounds for several cycles. 1 The figure above shows the position of the cart and the force on the cart as functions of time. a) Gross Behavior What features in the data shown above indicate that mechanical energy is not conserved? Although it is clear that mechanical energy is not conserved, it is not clear how and where the dissipation occurs. We will suggest a model for the energy loss, and let you determine if the model is consistent with the measured results. Assume the energy loss is due to two separate mechanisms. The first is rolling friction (see pages 155 and 328 in Young and Freedman, 12th edition) while the cart is not in contact with the spring. This could be caused by friction in the wheel bearings, friction between the wheels and sides of the grooves guiding the path of the car, or deformation of the wheels and track. Assume this gives rise to a friction force f that is constant in magnitude but always opposite in direction to the velocity of the cart. [We do not need to know howopposite in direction to the velocity of the cart....
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