A gymnast of mass 68.0 {\rm kg} 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 9.81 {\rm m/s^2} for the acceleration of gravity.
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To solve this problem, we need to find the tension in the rope while the gymnast is hanging.
Given data:
- Mass of the gymnast, m = 68.0 kg
- Acceleration due to gravity, g = 9.81 m/s^2
When the gymnast is hanging motionless from the rope, the tension in the rope, which acts upwards, balances the downward force due to the weight of the gymnast.
The weight of the gymnast can be calculated using the formula: weight = mass * acceleration due to gravity. In this case, weight = m * g.
Therefore, weight = (68.0 kg) * (9.81 m/s^2) = 666.48 N.
Since the rope is not stretching, the tension in the rope is equal to the weight of the gymnast.
So, the tension in the rope while the gymnast is hanging is 666.48 N.