Question

The weight of an object in space is 500 N. Use ratios to obtain the objects new weight at:A. Half the distance from the centre of the EarthB. At 1/8 the distance from the centre of the EarthC. At 0.66 the distance from the centre of the Earth

Answer 1

ANSWERS

A. 2000N

B. 32000N

C. 1147.8 N

EXPLANATION

In Newton's law of universal gravitation equation,

$F=G\cdot\frac{m_1m_2}{r^2}$

If we have the same two objects, but we change the distance between them, the factors G*m1*m2 remain constant,

$F\cdot r^2=Gm_1m_2=constant$

A. If the new distance, r2, is half the original distance of the object, r1, we have,

$F_1r^2_1=F_2r^2_2$

Knowing that r2 = 0.5r1, and that F1 is 500N, solve for F2,

$F_2=F_1\cdot\frac{r^2_1}{r^2_2}=500N\cdot\frac{r^2_1}{(0.5)^2r^2_1}=500N\cdot\frac{1}{0.25}=2000N$

B. Now, we have to do the same but in this case, r2 = 1/8r1,

$F_2=F_1\cdot\frac{r^2_1}{(1/8)^2r^2_1}=F_1\cdot8^2=500N\cdot64=32000N$

C. And finally, r2 = 0.66r1,

$F_2=F_1\cdot\frac{r^2_1}{(0.66)^2r^2_1}=500N\cdot\frac{1}{0.4356}\approx1147.8N$