A gymnast of mass 52.0 hangs from a vertical rope attached to the ceiling. You c

Question

A gymnast of mass 52.0 hangs from a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume that the rope does not stretch. Use the value for the acceleration of gravity. 1.Calculate the tension in the rope if the gymnast hangs motionless on the rope. 2.Calculate the tension in the rope if the gymnast climbs the rope at a constant rate. 3. Calculate the tension in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.30 . 4.Calculate the tension in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.30 . Please answer it is due at 8 and i am cramming.

Explanation / Answer

General case: Tension (T): upward Weight (m*g): downward Define acceleration positive when upward. T - m*g = m*a Solve for T: T = m*(g + a) Common data: m:=52.0 kg; g:=9.81 N/kg; Part A: a = 0, because gymnist is stationary Part B: a = 0, because gymnist is not accelerating, but climbing steadily Part C: a:=+1.30 m/s^2 Part D: a:= -1.30 m/s^2 Results: A) T = 510.12 Newtons B) T = 510.12 Newtons C) T = 577.72 Newtons D) T = 442.52 Newtons

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