How would the force of gravity between two masses be affected if the separation distance between them were the following? (Assume F2 represents the new force and F1 represents the original force.)(a) double the original distanceF2 / F1 = (b) one-third the original distanceF2 / F1 =

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Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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How would the force of gravity between two masses be affected if the separation distance between them were the following? (Assume F₂ represents the new force and F₁ represents the original force.)

(a) double the original distance
F₂ / F₁ =

(b) one-third the original distance
F₂ / F₁ =

Expert Solution

Step 1

Force of gravity is inversely proportional to the distance between two masses.

$F α \frac{1}{R^{2}} W h e r e, F = f o r c e R = d i s \tan c e b e t w e e n t w o m a s s e s$

Let, r₁ is the new distance and r is original distance

Therefore,

$\frac{F_{2}}{F_{1}} = \frac{r^{2}}{{(r_{1})}^{2}}$

(a) Double the original distance

That is r₁ = 2r

$\frac{F_{2}}{F_{1}} = \frac{r^{2}}{{(r_{1})}^{2}} P l u g i n r_{1} = 2 r \frac{F_{2}}{F_{1}} = \frac{r^{2}}{{(r_{1})}^{2}} = \frac{r^{2}}{{(2 r)}^{2}} = \frac{r^{2}}{4 r^{2}} = \frac{1}{4}$

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