A cube of polished steel sits on top of a highly polished and waxed hemisphere of polycarbonate (radius 92 cm). For these two surfaces interacting, the coefficient of kinetic friction is the same as the coefficient of static friction. The cube is given a very small 'nudge' perpendicular to the center of the cube and tangent to the top of the hemisphere. The cube starts to move with an initial speed. As the cube slides down the side of the sphere, it eventually loses contact with the surface of the sphere.
a.) Assume μ is zero and that the initial speed is also zero to solve for the angle (relative to the vertical) at which the cube falls off of the sphere.
b.) How does your answer to a change if the initial speed is not zero, but is 50cm/s? Discuss your results qualitatively (what changes and why) and describe them quantitatively (solve for the angle relative to the vertical at which the cube falls off).
c.) Assume that μ is 0.1 and that the initial speed is zero to solve for the angle.
d.) How does your answer to c change if the initial speed is not zero, but is 50cm/s? Discuss you results qualitatively (what changes and why) and describe them quantitatively (solve for the angle relative to the vertical at which the cube falls off).
I tried drawing a free body diagram and maybe looking at the forces that act on the cube but then I just got confused. Am I supposed to relate uniform circular motion into any of this? I attached a picture of the problem.
a.) Assume μ is zero and that the initial speed is also zero to solve for the angle (relative to the vertical) at which the cube falls off of the sphere.
b.) How does your answer to a change if the initial speed is not zero, but is 50cm/s? Discuss your results qualitatively (what changes and why) and describe them quantitatively (solve for the angle relative to the vertical at which the cube falls off).
c.) Assume that μ is 0.1 and that the initial speed is zero to solve for the angle.
d.) How does your answer to c change if the initial speed is not zero, but is 50cm/s? Discuss you results qualitatively (what changes and why) and describe them quantitatively (solve for the angle relative to the vertical at which the cube falls off).
I tried drawing a free body diagram and maybe looking at the forces that act on the cube but then I just got confused. Am I supposed to relate uniform circular motion into any of this? I attached a picture of the problem.
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