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/s2. The planet Neptune has radius RN = 24, 800 Km and mass MN = 1.03 × 1026 Kg.

a) What is the mass of the pumpkin?

b) What is the gravitational acceleration gP on the surface of Neptune?

c) What would be the mass and weight of the pumpkin at the surface of Neptune?

d) You now want to use the pumpkin as a satellite and place it in a circular orbit 1000 Km above Neptune’s surface. Compute the speed, the radial acceleration and the gravitational force acting on the satellite.

e) If you drive a small vehicle on the surface of Neptune on a turn of radius R = 160 m, and the coefficient of static friction between the wheels and the ground is s = 0.50, what is the maximum speed that you can reach without sliding sideways? Compare the result with the maximum speed that you can achieve on Earth (use the same values of s and R).

Explanation / Answer

a)

W = weight on earth = 58.8 N

g = acceleration due to gravity = 9.80

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

d)

r = 106 m

orbital speed = V = sqrt(GMp/r) = sqrt ((6.67 x 10-11) (1.03 x 1026) / (106)) = 8.3 x 104 m/s

radial acceleration = a = V2/r = (8.3 x 104 )2 / (106) = 6889

gravitational force

F = GMpm/r2 = (6.67 x 10-11) (1.03 x 1026) (6)/ (106)2 = 41220.6 N

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