At whаt temperаture (in °C) will 3.22 mоles оf а gas оccupy 86.1 L when the pressure is 1.51 atm? _______
A blоck is initiаlly аt pоsitiоn x = 0 аnd in contact with an uncompressed spring of negligible mass. The block is pushed back along a frictionless surface from position x = 0 to x = -D, as shown above, compressing the spring by an amount Δx = D. The block is then released. At x = 0 the block enters a rough part of the track and eventually comes to rest at position x = D. The coefficient of kinetic friction between the block and the rough track is μ. 1) Sketch and label a graph of the following two quantities as a function of the position of the block between x = -D and x = 3D. You do not need to calculate values for the vertical axis, but the same vertical scale should be used for both quantities. a) The kinetic energy of the block b) The elastic potential energy of the block-spring system. NOTE: When drawing this on your own paper, make sure that you include the x = -D, 0, x = D, etc. markings on the horizontal axis. 2) The spring is now compressed twice as much, to Δx = 2D. A student is asked to predict whether the final position of the block will be twice as far at x = 6D. The student reasons that since the spring will be compressed twice as much as before, the block will have more energy when it leaves the spring, so it will slide farther along the track before stopping at position x = 6D. a) Which aspects of the student's reasoning, if any, are correct? Explain how you arrived at your answer. b) Which aspects of the student's reasoning, if any, are incorrect? Explain how you arrived at your answer. 3) Derive an expression for the new final position of the block. Express your answer in terms of D. 4) Explain how any correct aspects of the student’s reasoning identified in parts 2a) and 2b) are expressed by your mathematical relationships in part 3. Explain how your relationships in part 3 correct any incorrect aspects of the student’s reasoning identified in parts 2a) and 2b).