4) On a lake, an ice skater having a constant 900 J of kinetic energy slides on

Question

4) On a lake, an ice skater having a constant 900 J of kinetic energy slides on the ice surface while holding on to a rope that frictionlessly slides about a vertical pole. Holding on to this rope keeps the skater a constant 3 m from the pole. Although we may take the tangential sliding motion in the circular path as frictionless (thus constant speed), the skater is leaning radially outward, and so digs his skates into the ice to keep his skates from slipping out from him. This action then pushes both vertically and radially inward upon the ice. The tension in the rope in this circumstance is 800 N. Digging into the ice implies that the ice will push upon the skater with a normal contact force at some angle. In essence, the skate blade slides upon an inclined plane that forms the edge of a circular path. The normal force of this inclined plane has then a vertical component vector that pushes upward to support the skater weight, and also a horizontal component vector that acts radially outward during the circular motion. Denote the magnitude of the radially outward component vector with R. a) Determine the product of the skater mass and the square of the speed of the skater. b) List what distinct horizontal forces act upon the ice skates (and thus upon the skater), and their direction. However, avoid including in this list any force twice in any manner. c) Determine the magnitude of the outward radial force R of the ice on the skater. To BoDN

Explanation / Answer

(A) K E = m v^2 / 2 = 900 J

mv^2 = 1800

(B) Tension force -> toward the pole   

normal force's horizontal component (R) -> radilly awat from pole

(C) in horizontal, T - R = m a = m v^2 / r

800 - R = (1800)/3 = 600

R = 200 N ........Ans

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