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If the mass of a certain object is 78 kg, determine its weight on the surface of the earth in pounds. (Round the final answer to three decimal places.)

A) 171.962 lbs
B) 171.962 lb
C) 172 lbs
D) 172 lb

Answer :

Final answer:

The weight of an object with a mass of 78 kg on Earth is calculated by first converting kilograms to Newtons and then Newtons to pounds. After rounding to three decimal places, it gives a value of 168.776 lbs. However, the provided answer choices in the question contain an error as none match the calculated value. The correct option is not listed here.

Explanation:

The question is asking to calculate the weight of an object given its mass on Earth. To convert mass (in kilograms) to weight (in pounds), we use the fact that on Earth, a mass of 1 kg corresponds to a weight of approximately 9.8 Newtons due to gravity. On Earth, 1 pound (lb) is equivalent to 0.4536 kilograms. Therefore, to find the weight in pounds, we divide the mass in kilograms by this conversion factor and then multiply by the acceleration due to gravity. For our specific case, the object has a mass of 78 kg. To find its weight on the surface of the Earth in pounds, we do the following calculation:

  • Convert the mass from kilograms to Newtons by multiplying by the acceleration due to gravity: 78 kg × 9.8 m/s² = 764.4 N (Newton).
  • Convert Newtons to pounds by dividing by the weight equivalent of a kilogram in pounds: 764.4 N / (9.8 m/s² × 0.4536 kg/lb) = 168.776 lbs

Now that we have the weight in pounds, we need to round the result to three decimal places, which gives us 168.776 lbs. When written as an answer choice, this would be listed without units as just the numerical part, hence the correct answer would be 'B) 171.962' if we were to assume no typo in the options provided. However, considering the calculations, none of the provided answer choices are correct. The correctly calculated value should be '168.776 lbs'.

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