Question #103559
A space traveler weighs 540.0 N on earth. Calculate what the travelers will weigh on another planet whose radius is four that of the earth and whose mass is five times that of earth ?
1
Expert's answer
2020-02-24T10:41:12-0500

Let's write the formula for the gravitational acceleration on Earth:


gE=GMERE2,g_E = \dfrac{GM_E}{R_E^2},

here, GG is the gravitational constant, MEM_E is the mass of the Earth, RER_E is the radius of the Earth.

Then, we can write the gravitational acceleration on another planet in terms of gEg_E :


gp=GMpRp2=5GME(4RE)2=5GME16RE2=516gE.g_{p} = \dfrac{GM_p}{R_p^2} = \dfrac{5GM_E}{(4R_E)^2} = \dfrac{5GM_E}{16R_E^2} = \dfrac{5}{16}g_E.

Finally, we can find the weight of the space traveler:


Wtraveler,p=mgp=516mgE=516Wtraveler,E=516540N=169N.W_{traveler, p} = mg_p = \dfrac{5}{16}mg_E = \dfrac{5}{16}W_{traveler,E} = \dfrac{5}{16} \cdot 540N = 169N.

Answer:

Wtraveler,p=169N.W_{traveler, p} = 169N.


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