Gnarls B.

asked • 11/16/17

Newton's gravity and weight qs

An astronaut has a mass of 80 kg, but on an unknown planet, the bathroom scale reads 15 kg when the astronaut stands on it. What is the astronaut's weight and the gravitational field strength on the unknown planet?

1 Expert Answer

By:

Arturo O. answered • 11/16/17

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Gnarls B.

Why do you need to divide the lighter mass by the heavier? I'm getting the same answer when I do (15 x 9.8)
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12/09/17

Arturo O.

The apparent mass on the planet is lower than the mass on the earth by a factor of 15/80.  But since the mass must be the same on the earth and on the planet, the gravitational acceleration on the planet must be lower by the same factor of 15/80.  On either the earth or the planet, the scale measures weight, not mass.
 
weight on earth:  mg = (80)(9.8) N
weight on planet:  mg' = (80)g'
 
(weight on planet)/(weight on earth) = 15/80
 
(weight on planet)/(weight on earth) = g'/9.8
 
g'/9.8 = 15/80
 
g' = 9.8(15/80) m/s2 = 1.8375 m/s≅ 1.84 m/s2
 
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12/09/17

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