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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 (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 mm is set to 15.0 kg and allowed to fall through 5.00m, it gives 250.0 J of kinetic energy to the drum.

A) If the system is operated on Mars, through what distance would the 15.0 kg mass have to fall to give the same amount of kinetic energy to the drum?

B) How fast would the 15.0 kg mass be moving on Mars just as the drum gained 250.0 J of kinetic energy?

Correct 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 (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 15.0 kg and allowed to fall through 5.00 m, it gives 250.0 J of kinetic energy to the drum.

Part B How fast would the 15.0 kg mass be moving on Mars just as the drum gained 250.0 J of kinetic energy? Express your answer with the appropriate units. Figure < 1 of 1 > 622 Drum Submit Previous Answers Request Answer * Incorrect; Try Again; 24 attempts remaining Provide Feedback

Answer “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 (Figure 1)”.

Kinetic Energy:

An item’s kinetic energy is the amount of energy it generates from its movement. It refers to the work required to propel a body with a given mass from its rest to its expressed speed. Motor energy equals 1/2 of the sum of the mass and square of speed.

Answer and Explanation:

Given data:

• Mass m =15.0kg

• The acceleration due to gravity on mars g_m = 3.71m/s²
• Falling height of earth h_E = 5.00m
• Kinetic energy to the drum is E = 250.0J

Part A) We know from the conservation of energy that all energy lost due to falling objects is converted to kinetic translational energy and rotational kinetic energie E. This is:

We know that the angular velocity is ω

The potential energy to the left is the same as it is on earth or on Mars. We can therefore write:

Where,

g_E and g_m  is acceleration due to gravity on earth, mars

h_E and h_m is fall height of earth and mars.

The relation for the mars fall height is as follows:

Now we get:

Part B)

Mass m=15.0kg

The drum gained kinetic energy E = 250.0 J

Use the velocity relation:

Last words

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