The sketch below shows a ball of mass m on a spring of unextended length Ro...

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The sketch below shows a ball of mass m on a spring of unextended length Ro and spring constant k. The spring is pivoted on the left on a central axis marked with a cross. The axis is perpendicular to the plane of the sketch. The ball and spring rotate around the central axis on a smooth horizontal table as indicated by the arrow in the sketch. The spring will break if it is stretched with a force larger than Fmax- R m (a) Find the equilibrium extension R of the system when it rotates with angular frequency w. (b) Find the equilibrium angular frequency we at which the spring will break. (c) Sketch we against Fmar in the range from zero to one Newton for the following parameters m = 1 kg, Ro 1 m, k = 1 Nm-¹. Label your axes. = (d) Under some conditions the system can only achieve a maximum angular frequency wiwe. Find a relationship between k, m and w, and explain what happens to the system as the angular frequency increases to w. [3] [2] The sketch below shows a ball of mass m on a spring of unextended length Ro and spring constant k. The spring is pivoted on the left on a central axis marked with a cross. The axis is perpendicular to the plane of the sketch. The ball and spring rotate around the central axis on a smooth horizontal table as indicated by the arrow in the sketch. The spring will break if it is stretched with a force larger than Fmax- R m (a) Find the equilibrium extension R of the system when it rotates with angular frequency w. (b) Find the equilibrium angular frequency we at which the spring will break. (c) Sketch we against Fmar in the range from zero to one Newton for the following parameters m = 1 kg, Ro 1 m, k = 1 Nm-¹. Label your axes. = (d) Under some conditions the system can only achieve a maximum angular frequency wiwe. Find a relationship between k, m and w, and explain what happens to the system as the angular frequency increases to w. [3] [2]

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