Question

Engineers are designing a system by which a falling mass m 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 m/s^2 In the earth tests, when m is set to 13 0 kg and allowed to fall through 5 00 m it gives 150.0 J of kinetic energy to the drum. If the system is operated on Mars through what distance would the 13 0-kg mass have to fall to give the same amount of kinetic energy to the drum? How fast would the 13 0-kg mass be moving on Mars just as the drum gained 150 0 J of kinetic energy?

Answer 1

On earth :

I = moment of inertia of drum

r = radius of drum

w = angular speed of drum

h = height travelled by mass "m" = 5 m

v = speed gained by mass "m"

using conservation of energy

kinetic energy of mass "m" + Rotational KE of drum = Potential energy lost by mass "m"

(0.5) m v² + 150 = mg h

(0.5) (13) v² + 150 = (13) (9.8) (5)

v = 8.7 m/s

On mars :

I = moment of inertia of drum

r = radius of drum

w = angular speed of drum

h = height travelled by mass "m"

v = speed gained = 8.7 m/s

using conservation of energy

kinetic energy of mass "m" + Rotational KE of drum = Potential energy lost by mass "m"

(0.5) m v² + 150 = mg h

(0.5) (13) (8.7)² + 150 = (13) (3.71) h

h = 13.31 m

b)

v = 8.7 m/s