An acrobat, starting from rest, swings freely on a trapeze of length 3.7m. If the initial angle of the trapeze is 48 degrees, use the law of conservation of energy to determine the acrobat's speed...

An acrobat, starting from rest, swings freely on a trapeze of length 3.7m. If the initial angle of the trapeze is 48 degrees, use the law of conservation of energy to determine the acrobat's speed at the bottom of the swing and the maximum height, relative to the initial position, to which the acrobat can rise.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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An acrobat, starting from rest, swings freely on a trapeze of length 3.7 m. The initial angle of the trapeze is 48 degrees. As the length of the trapeze is 3.7 m, the height of the acrobat from the lowest point of the trapeze at the initial point is 3.7 - 3.7*cos 48. If the acrobat has a mass M, the potential energy of the acrobat is M*9.8*(3.7 - 3.7*cos 48). At the bottom of the swing, the acrobat has a speed v such that (1/2)*M*v^2 = M*9.8*(3.7 - 3.7*cos 48)

=> v^2 = 19.6*(3.7 - 3.7*cos 48)

=> v = 4.89 m

As no energy is being added to the system, the acrobat can only reach a height equal to the that at the initial position. The maximum height to which the acrobat can rise relative to the initial position is 0.

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