Engineers are designing a system by which a falling mass imparts kinetic energy

Question

Engineers are designing a system by which a falling mass imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum (the figure (Figure 1) ). There is no appreciable friction in the axle of the drum, and everything starts from rest. This system is being tested on earth, but it is to be used on Mars, where the acceleration due to gravity is 3.71 . In the earth tests, when is set to 18.0 and allowed to fall through 6.00 , it gives 300.0 of kinetic energy to the drum. How fast would the 18.0-mass be moving on Mars just as the drum gained 300.0 of kinetic energy? (Answer not 5.77)

Explanation / Answer

Distance travelled by the mass:

Distance = 6*9.81/3.71

= 15.85 m

Potential energy = Kinetic rotational + kinetic linear

Kinetic rotational= 300.0

18*3.71*15.85=300+0.5*18*V^2

V = 9.18 m/s OR 9.2 m/s

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