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Chapter 1: Q37E (page 427)

The acceleration due to gravity at the north pole of Neptune is approximately11.2m/s2. Neptune has mass1.02脳1026km and radius2.46脳104km and rotates once around its axis in about 16 h.

(a) What is the gravitational force on a3.00 kgobject at the north pole of Neptune?

(b) What is the apparent weight of this same object at Neptune鈥檚 equator? (Note that Neptune鈥檚 鈥渟urface鈥� is gaseous, not solid, so it is impossible to stand on it.)

Short Answer

Expert verified

The apparent weight of the Neptune is 32.7 N.

Step by step solution

01

Identification of the given data

The given data can be listed below as,

  • The gravity is, =11.2m/s2
  • The mass is, =1.02脳106km
  • The radius is, =2.46脳104km2.46脳104km
  • The surface is gaseous, not solid, so it is impossible to stand on it.
02

The gravitational force on a object at north pole of Neptune

Gravitational force,

F = mg

Here, m is the mass of the Neptune, g is the gravity of the Neptune.

Substitute all the values in the above equation.

F=mgF=3脳11.2=33.6N

03

The apparent weight of the object at Neptune’s equator

Apparent weight at the equator = m(g-a)

a = centripetal acceleration at equator = R蝇2

16hr=57600s蝇=2蟺T=2蟺57600s=1.1脳10鈭�4rad/seca=R蝇2=0.0246脳106脳1.1脳10鈭�42=0.297鈮�0.30m/s2

Apparent weight = m(g-a)

=3a11.2-0.3=32.7N

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