True mass, different weights, and the force of gravity

In summary, an astronaut travels to a new planet with a mass 2.5 times that of Earth and a radius 1.2 times that of Earth. If the astronaut has a weight of 60.0kg on Earth, their weight on the new planet would be 103.4kg. The scale on Earth displays the astronaut's true mass, as it measures weight and calculates mass, but this only works on Earth.
  • #1
sdoi
37
0

Homework Statement


An astronaut enters a rocket ship and gets blasted to another planet. The mass of the planet is 2.5 times as large as the mass of Earth, and the radius is 1.2 times as large as Earth's. If the astronauts scale at home says "60.0kg", what will it say on the new planet? In which case does the scale display his true mass and why?


Homework Equations


F=mg/r^2


The Attempt at a Solution


i was able to find the weight of the astronaut on the new planet without any problems:
m(planet)= m(earth) x 2.5
m(planet)= 1.48x10^25 kg

r(planet)= r(earth) x 1.2
r(planet)= 7.65x10^6m

find mass of astronaut:
F=Gm/r^2
g=Gm/r^2
= (6.67x10^-11)(5.97x10^24)/ (6.38x10^6)^2
=9.8N/kg
m= 60.0kg/ 9.8N/kg
m=6.12N

g= Gm/r^2
= (6.67x10^-11)(1.49x10^25)/ (7.65x10^6)^2
= 16.9 N/kg

W=mg
= (6.12N)(16.9 N/kg)
Therefore the atronaut would read 103.4kg on the scale while on the new planet.

For the second part of the question I'm just a little confussed. It asks which scale displays his true mass, but a scale doesn't display mass, it displays weight. Is this part a trick question?
 
Physics news on Phys.org
  • #2
I would say the scale shows the true mass on earth. In fact, it measures weight, but from the measured weight, it calculated the mass and shows it. But it works only on earth.
 

What is true mass?

True mass refers to the actual amount of matter present in an object, which is measured in kilograms (kg). It is a fundamental property of an object and does not change, regardless of its location or environment.

How is mass different from weight?

Mass and weight are often used interchangeably, but they are actually two different quantities. Mass is a measure of the amount of matter in an object, while weight is a measure of the force exerted on an object by gravity. Mass is constant, but weight can change depending on the strength of the gravitational pull on an object.

What is the force of gravity?

The force of gravity is the attractive force between two objects with mass. It is responsible for keeping objects in orbit around larger bodies, such as planets orbiting the sun. The strength of the force is determined by the mass of the objects and the distance between them.

Does gravity affect all objects equally?

Yes, gravity affects all objects with mass equally. However, objects with larger masses will have a stronger gravitational pull on other objects compared to objects with smaller masses.

How does the force of gravity change with distance?

The force of gravity decreases as the distance between two objects increases. This is described by the inverse square law, which states that the force of gravity is inversely proportional to the square of the distance between the objects. This means that the farther apart two objects are, the weaker the force of gravity between them will be.

Similar threads

Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
449
  • Introductory Physics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
4K
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Classical Physics
Replies
7
Views
744
  • Introductory Physics Homework Help
Replies
11
Views
1K
Back
Top