A large pumpkin has a weight W = 58.8 N when measured on the Earth where g = 9.8

Question

A large pumpkin has a weight W = 58.8 N when measured on the Earth where g = 9.80 m/s^2. The planet Neptune has radius R_N = 24, 800 Km and mass M_N =. 1.03 times 10^26 Kg. a) What is the mass of the pumpkin? b) What is the gravitational acceleration g_p on the surface of Neptune? c) What would be the mass and weight of the pumpkin at the surface of Neptune ? d) If you attach a the pumpkin to a vertical spring with elastic constant k = 1.800 N/m, how much would the spring stretch on the Earth? How much on Neptune?

Explanation / Answer

a)

Given Data W = weight on earth = 58.8 N

g = acceleration due to gravity = 9.80

Solution:-

m = mass on earth = W/g

                              = 58.8/9.80

                             = 6 kg

b)

gp = GMp/Rp2

      = (6.67 x 10-11) (1.03 x 1026) / (24800 x 103)2

       = 11.2 m/s2

c)

at neptune . m = 6 kg   ,

since mass does not change on any planet

weight = Wp = m gp

                         = 6 (11.2)

                   = 67.2 N

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