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Why is the following situation impossible?

An athlete tests her hand strength by having an assistant hang weights from her belt as she hangs onto a horizontal bar with her hands. When the weights hanging on her belt have increased to 80% of her body weight, her hands can no longer support her, and she drops to the floor.

Frustrated at not meeting her hand-strength goal, she decides to swing on a trapeze. The trapeze consists of a bar suspended by two parallel ropes, each of length \( l \), allowing performers to swing in a vertical circular arc. The athlete holds the bar and steps off an elevated platform, starting from rest with the ropes at an angle \(\theta_i = 60.0^\circ\) with respect to the vertical. As she swings several times back and forth in a circular arc, she forgets her frustration related to the hand-strength test.

Assume the size of the performer's body is small compared to the length \( l \) and air resistance is negligible.

Answer :

The given situation is impossible because the athlete could not even hang on the horizontal bar when the weights hanging on her belt have increased to 80% of her body weight, which means the force required to support her is greater than her body weight.

If she couldn't even lift her own body weight, it is impossible for her to use her hand strength to swing on the trapeze, which is much more difficult than just hanging from the horizontal bar.

The situation is a classical example of work done by a force in physics.

Work done by a force is equal to the product of force and displacement. If the force is less than the weight of the object, the work done will be less than the gravitational potential energy of the object.

This means that the object will not gain enough kinetic energy to move to a higher position.

The athlete cannot lift her own body weight, which means that the force she can exert on the trapeze bar will be less than her body weight.

The force required to lift her body weight is much greater than the force required to support her body weight, which means that it is impossible for her to swing on the trapeze bar.

Therefore, the given situation is impossible. The athlete could not even hang on the horizontal bar when the weights hanging on her belt have increased to 80% of her body weight, which means the force required to support her is greater than her body weight.

Learn more about: body weight

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