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HW7: Conservation of Energy Due 11/9/2021 1) See the final project assignment on canvas. Submit a final project proposal to the project proposal assignment under canvas. Your proposal should include. a) A few sentences describing your proposed topic b) How your topic relates to physics c) How you plan to understand the physics behind your topic d) Two references 2) A mass of m = 0.5 kg slides down a frictionless ramp from an initial height of 2 meters. Then the mass slides along the floor. a) What is the potential energy of the mass? What kind of potential energy does the mass have? b) How fast is the mass moving at the bottom of the ramp? c) If there is no friction on the floor, how far will the mass travel? d) If the coefficient of kinetic friction is .25 i) Find the frictional force acting on the mass ii) How far will the mass slide along the floor (Hint: How much work needs to be done so the mass has no energy) e) Where do you think the lost due to friction energy goes? 3) A pendulum is lifted to a height h above its lowest point, as depicted in the image below. a) If the initial height of the pendulum is 0.1 m, find its maximum speed. b) If the length, L, of the string attached to the mass is quadrupled, by how much will the period increase? c) Describe how a pendulum can be used to measure time. 4) Consider a mass m attached to a spring of constant k on a frictionless horizontal plane, as shown below. a) If k = 25 N/m, m = 0.3 kg, and the mass is displaced by an initial distance of x = 0.05 m, what is its maximum speed? b) Using the same parameters from part b, find the speed of the mass when it reaches a displacement of x = 0.025 m.

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