Subjective Type

In Fig 13-34, three 5.00 kg spheres are located at distances $$ d_{1} $$=0.300 m and $$ d_{2} $$= 0.400 m . what are the (a) magnitude and (b) direction (relative to positive direction of the x axis ) of the net gravitational force on sphere B due to sphere A and C

Solution

we know $$F = GmM/r_2 $$,

$$F_A=\dfrac{G5\times 5}{0.3^2}$$

$$F_A=1.9 \times 10 ^{-8} N$$,
and
$$F_C=\dfrac{G5\times 5}{0.4^2}$$

$$F_C=1.0 \times 10 ^{-8} N$$,

we find that the topmost mass pulls upward on the one at the
origin with $$1.9 \times 10 ^{-8} N$$, and the rightmost mass pulls rightward on the one at the origin with $$1.0 \times 10 ^{-8} N$$.

Thus, the (x, y) components of the net force, which can be converted to
polar components (here we use magnitude-angle notation), are

$$\vec{F_{net}}=(1.9 \times 10 ^{-8} ,1.0 \times 10 ^{-8} )$$

magnitude = $$\sqrt{(1.0\times 10^{-8})^2+(1.9\times 10^{-8})^2}=2.13\times 10^{-6}$$

angle = $$\tan^{-1}\dfrac{1.0\times 10^{-8}}{1.9\times 10^{-8}}=60.6^o$$

The direction of the force relative to the +x axis is $$\angle 60.6^o$$

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