Question

An astronaut weighing 259 lbs on Earth is on a mission to the Moon and Mars. (a) What would he weigh in newtons when he is on the Moon? The acceleration due to gravity on the Moon is one-sixth that on Earth. 0.043 Incorrect: Your answer is incorrect. seenKey 192 Weight is the gravitational force exerted on an object. Recall the formula for weight and the quantities it depends on. Which quantity is the same on the Earth as on the Moon? Which quantity changes on the Moon? Also note your answer should be in newtons. N (b) How much would he weigh in newtons when he is on Mars, where the acceleration due to gravity is 0.38 times that on Earth? N (c) What is his mass in kilograms on Earth? kg

Answer 1

Answers:

a) 191.884 N

b) 437.495 N

c) 117.48 kg

Step-by-step explanation:

Let's start by defining what is mass and weight:

The mass is the amount of matter that exists in a body, which only depends on the quantity and type of particles within it. This means mass is an intrinsic property of each body and remains the same regardless of where the body is located.

Weight is the force that gravity exerts on matter and changes depending on where the body is located. Therefore, the weight of an object on Earth will not be the same as the weight of the same object on the Moon or on Mars.

Having this clear, let's begin with the answers:

Weight
`W` is mathematically expressed as:

`W=m.g`

Where
`m` is the mass of the body (which does not change with the location) and
`g` is the acceleration due gravity in each place.

In this case the mass of the astronaut is:

`m=259 lb (0.453592 kg)/(1 lb)=117.48 kg`

And the acceleration due gravity is:

On Earth:
`g_(EARTH)=9.8 m/s^(2)`

On the Moon:
`g_(MOON)=(1)/(6)g_(EARTH)=(1)/(6)(9.8 m/s^(2))=1.633m/s^(2)`

On Mars:
`g_(MARS)=0.38 g_(EARTH)=0.38 (9.8 m/s^(2))=3.724m/s^(2)`

a) Weight of the astronaut on the Moon

In this case the equation is:

`W_(MOON)=m.g_(MOON)`

`W_(MOON)=(117.48 kg)(1.633m/s^(2))`

`W_(MOON)=191.884 N`

b) Weight of the astronaut on Mars

For Mars the equation is:

`W_(MARS)=m.g_(MARS)`

`W_(MARS)=(117.48 kg)(3.724m/s^(2))`

`W_(MARS)=437.495 N`

c) Mass of the astronaut

As we said before, the mass of the astronaut does not change and is 117.48 kg