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2 years ago

4

Saturn’s moon Titan has a mass of 1.35 × 1023 kg. If Titan is 1.19 × 106 km from Saturn, and Saturn’s mass is 5.86 × 1026 kg, wh

at is the gravitational force between Saturn and its moon?
2.76 × 104 N
3.29 × 107 N
3.73 × 1021 N
4.43 × 1030 N

2 answers:

djyliett [7]2 years ago

5 0

3.73 x 10^21 N. Find gravitational force m1xm2/d^2

Deffense [45]2 years ago

3 0

The gravitational force equation is Fg=(G*M*m)/r² where, G is the gravitational constant, G=6.67*10^-11 m³/kg*s², M is the mass of Saturn, M=5.86*10^26, m is the mass of Titan, m=1.35*10^23 and r is the distance, r=1.19*10^6 km=1.19*10^9 m. Now we simply input the numbers into the equation:

Fg=(6.67*10^-11)*(5.86*10^26)*(1.35*10^23)/(1.19*10^6)²
Fg=(5.277*10^39)/(1.41*10^18)=3.743*10^21 N

The correct answer is the third one.

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Explanation:

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System diagram for given situation is shown in attached Fig. 1

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<h3>PROOF:</h3>

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Put (4) and (1) in (2)

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from Fig 3 it can be seen that fs is force by which the cylinders roll without slipping as they oscillate

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Using (6) in (8)

$\frac{1}{2}Ma_{x} - kx =Ma_{x}$

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$a= -\omega^{2} x$ ----- (10)

Equating (9) and (10)

$\omega^{2} = \frac{2k}{3M}$

$\omega = \sqrt{ \frac{2k}{3M}}$

then (9) becomes

$a_{x} = - \omega^{2}x$

(The minus sign says that x and aₓ have opposite directions as shown in fig 3)

This proves that the motion of the center of mass of the cylinders is simple harmonic.

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Answer:

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Answer:

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