Question

Two blocks are attached to one another, as shown, by means of a massless cord that passes over a massless frictionless pulley. Block 1 (mass m1, = 10.0 kg) is connected to a spring with spring constant k = 100 N/m, and block 2 (mass m2 = 20.0 kg) sits on a frictionless ramp that makes an angle theta = 30.0 degree with the horizontal. The coefficient of kinetic friction between block 1 and the horizontal surface is mu k = 0.10. Both blocks are initially at rest. For this problem, approximate the magnitude of acceleration due to gravity as g = 10.0 m/s2. Write an expression for U(x), the total potential energy of the system, as a function of x, the displacement of the spring from its relaxed length. Set gravitational potential energy of the blocks-earth-spring-ramp system to be zero when the spring is relaxed. Plot U(x) on the graph paper provided, clearly labelling all important values of x and J(x). Plot U(x) using a regular pencil or black ink, or use a dark solid line. When released, the blocks move rightward and down the ramp, momentarily coming to rest before block 1 can hit the pulley. Write an expression for E(x), the mechanical energy of the blocks-earth-spring-ramp system during this movement. Plot E(x) on the graph paper below, using the same scale and axes used for U(x). Use your plot to estimate xstop, where the system comes to rest. Indicate this value on your plot. Plot E(x) using a colored pencil or colored ink, or use a dashed line, in order to distinguish it from U (x). Use conservation of total energy for the blocks-earth-spring-ramp system to verify the value of xstop that you estimated in part (b).

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Answer 1