Question

The acceleration due to gravity at the north pole of Neptune is approximately 11.2m/s2. Neptune has mass 1.02×1026kg and radius 2.46×104km and rotates once around its axis in about 16 h. (a) What is the gravitational force on a 3.00-kg object at the north pole of Neptune? (b) What is the apparent weight of this same object at Neptune’s equator? (Note that Neptune’s "surface" is gaseous, not solid, so it is impossible to stand on it.)

Answer 1

Answer:

(a) F(gravitational force)=33.7 N

(b) W (Weight)=32.8 N

Explanation:

Given Data

a=11.2 m/s²

m (Neptune mass)=1.02*10²⁶ kg

r=2.45*10⁴ km

t=16 h

(a) Gravitational Force=? when m₁=3.0 kg

(b) Weight=?

Solution

For part (a) gravitational force

$F=\frac{Gmm}{R^{2} }\\ G=6.67*10^{-11}\frac{Nm^{2} }{kg^{2} }\\ F=\frac{6.67*10^{-11}*1.02*10^{26}*3.00 }{(2.46*10^{4} *1000)^{2} }\\ F=33.7N$

For (b) part Weight

$W=F-\frac{mv^{2} }{R}\\ as\\T=\frac{2*\pi *r}{V}\\ V=\frac{2*\pi *r}{T}\\ V=\frac{2*(3.14)*(2.46*10^{4} *1000)}{16*3600} \\V=2683 \frac{m}{s}$

V=2683 m/s

$W=33.7-\frac{3*(2683)^{2} }{2.46*10^{4}*1000 }\\ W=32.8N$