Answer:
Approximately [tex]262\; {\rm kg}[/tex], assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] on Earth, and that the weight lifter delivers the same maximum upward force on Mars as on Earth.
Explanation:
Assuming that the weight-lifter delivery the same upward force on Mars as on Earth, apply the following steps to find the mass that can be lifted on Mars:
- Using the gravitational field strength on Earth and the maximum mass that can be lifted on Earth, find the maximum upward force that the weight lifter can exert.
- Divide the maximum upward force (maximum weight of the mass) by the gravitational field strength on Mars to find the maximum mass that can be lifted on Mars.
To lift a [tex]100\; {\rm kg}[/tex] mass on Earth, the weight lifter needs to deliver an upward force equal to the weight of that mass.
The weight of an object on a planet is equal to the gravitational attraction that the planet exerts on the object. If the gravitational field strength is [tex]g[/tex], the weight of an object of mass [tex]m[/tex] would be [tex]m\, g[/tex]. Hence, assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] on Earth, the weight of the [tex]100\; {\rm kg}[/tex] mass on Earth would be:
[tex]m\, g = (100\; {\rm kg})\, (9.81\; {\rm m\cdot s^{-2}}) = 981\; {\rm N}[/tex].
(Note that [tex]1\; {\rm N} = 1\; {\rm kg\cdot m\cdot s^{-2}}[/tex].)
In other words, the maximum upward force that this weight lifter can deliver would be [tex]981\; {\rm N}[/tex]. Thus, the weight of the heaviest object that this weight-lifter can lift on Mars would be equal to [tex]981\; {\rm N}[/tex]. To find the mass of this object, divide the weight of the object on Mars by the gravitational field strength on Mars:
[tex]\displaystyle \frac{981\; {\rm N}}{3.75\; {\rm m\cdot s^{-2}}} \approx 262\; {\rm kg}[/tex].
Thus, under the assumptions, the maximum mass that this weight-lifter can lift on Mars would be approximately [tex]262\; {\rm kg}[/tex].
