Block A is comprised of quartz and has a mass of 25 kg, ramp B is...
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Block A is comprised of quartz and has a mass of 25 kg, ramp B is comprised of smooth granite. The two materials are subjected to a simple ramp sliding test, as shown in Fig. 1, to estimate the coefficient of friction. Determine the following: a) Draw the free body diagram and mass/acceleration diagram for block A. b) Write the resulting equations of motion for block A. c) Determine an expression for the static coefficient of friction as a function of the ramp angle when the system is in equilibrium (i.e., when Σ F = 0). d) Estimate the static coefficient of friction if block A just begins to slide with a constant velocity at an average angle of 0 = 24°. e) Estimate the average kinetic coefficient of friction if block A accelerates at 1.9 m/s², 2.7 m/s² and 3.1 m/s² down the ramp when tilted at angles of 24.1°, 27°, and 30°, respectively. HINT: Return to the general equations from part (b) B Fig. 1: Schematic of the friction ramp test. A Block A is comprised of quartz and has a mass of 25 kg, ramp B is comprised of smooth granite. The two materials are subjected to a simple ramp sliding test, as shown in Fig. 1, to estimate the coefficient of friction. Determine the following: a) Draw the free body diagram and mass/acceleration diagram for block A. b) Write the resulting equations of motion for block A. c) Determine an expression for the static coefficient of friction as a function of the ramp angle when the system is in equilibrium (i.e., when Σ F = 0). d) Estimate the static coefficient of friction if block A just begins to slide with a constant velocity at an average angle of 0 = 24°. e) Estimate the average kinetic coefficient of friction if block A accelerates at 1.9 m/s², 2.7 m/s² and 3.1 m/s² down the ramp when tilted at angles of 24.1°, 27°, and 30°, respectively. HINT: Return to the general equations from part (b) B Fig. 1: Schematic of the friction ramp test. A
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