Which of these objects would have greater mass, object A that weighs 50N on earth or object B with a weight of 50N on the moon?

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Which of these objects would have greater mass, object A that weighs 50N on earth or object B with a weight of 50N on the moon?

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Answer 1 · 2017-07-28T16:07:59

Object B (The object on the Moon)

Explanation:

We're asked to find which of two objects has a greater mass, given that they have the same weight on two different celestial bodies.

Recall Newton's second law, which states

$\sum \to F = m \to a$ $sumvecF = mveca$

We need to know the magnitude of the acceleration $g$ $g$ for each body. We know earth's is $9.81$ $9.81$ ${m/s}^{2}$ $"m/s"^2$ , and the Moon's is $1.624$ $1.624$ ${m/s}^{2}$ $"m/s"^2$ (from Internet or any resource).

Earth:

We have

$\sum F = 50$ $sumF = 50$ $N$ $"N"$ (weight)
$a = 9.81$ $a = 9.81$ ${m/s}^{2}$ $"m/s"^2$

Thus,

$m = \frac{\sum F}{a} = 5.10$ $m = (sumF)/a = color(red)(5.10$ $g$ $color(red)("g"$

Moon:

We have

$\sum F = 50$ $sumF = 50$ $N$ $"N"$ (weight)
$a = 1.624$ $a = 1.624$ ${m/s}^{2}$ $"m/s"^2$

So

$m = \frac{\sum F}{a} = 30.8$ $m = (sumF)/a = color(blue)(30.8$ $g$ $color(blue)("g"$

Thus, object $sfcolor(blue)("B"$ has the greater mass.

Answer 2 · 2017-07-29T12:00:08

B

Explanation:

Intuitively, since gravity on the moon is less than that on Earth, it takes more mass on the moon to produce the same force.

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Which of these objects would have greater mass, object A that weighs 50N on earth or object B with a weight of 50N on the moon?

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