Exercise 9.68 Engineers are designing a system by which a falling mass m imparts

Question

Exercise 9.68

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/s2. In the earth tests, when m is set to 14.0 kg and allowed to fall through 5.00 m , it gives 150.0 J of kinetic energy to the drum.

Part A

If the system is operated on Mars, through what distance would the 14.0-kg mass have to fall to give the same amount of kinetic energy to the drum?

Part B

How fast would the 14.0-kg mass be moving on Mars just as the drum gained 150.0 J of kinetic energy?

Explanation / Answer

PART - A : W = F X S ( work done = force x displacement )

                 I n this case work done stored in the form of kinetic energy

                that is 1/2 m v2 = F x S          GIVEN : K.E = 150 J , m = 14 k.g

                          150 = mg x S              since g = 3.71 m / sec2

                          150 = 14 x 3.71 x S

                          therefore S = 150 / 51.94

                                         S = 2.88 m

PART ( B ) : K . E = 150

                   1/ 2 m v2 = 150

                     v2 = 2 x 150 / m since m = 14 k.g

                     v2 = 300 / 14

                    v2    = 21 . 4285

                    v = 4. 6290 m / Sec

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