Physics, 21.07.2019 13:00 jandrew2052

(a) find the magnitude of the gravitational force between a planet with mass 7.50 3 1024 kg and its moon, with mass 2.70 3 1022 kg, if the average distance between their centers is 2.80 3 108 m. (b) what is the acceleration of the moon towards the planet? (c) what is the acceleration of the planet towards the moon?

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The magnitude of the gravitational force between two bodies is the product of their masses divided by the square of the distance between them. So we have F = M1*M2 / r^2. M1 = 7.503 * 10e24 and M2 = 2.703 * 10e22 and r= 2.803 * 10e8; r^2 = 5.606 *10e16. So we have 7.503 *2.703 *10^(24+22) = 20.280 * 10^(46). Then we divide our answer by 5.606 * 10e16 which is the distance ; then we have 3.6175 * 10 e (46- 16) = 3.6175 * 10e30. To find the acceleration we use Newton's second law F = ma. F is 3.6175 * 10e30 and M is 7.503 * 10e24 so a = F/M and then we have 3.6175/7.503 * 10e (30-24) = 0.48 * 10e6. Similarly for moon, we have a = 3.6715/2.703 * 10e(30-22). = 1.358 * 10e8

Answer from: titofigueroa777

(a) The magnitude of gravitational force between the moon and planet is $1.721 \times 10^{20} \;\rm N$ .

(b) The acceleration of moon towards the planet is $6.36 \times 10^{-3} \;\rm m/s^{2}$ .

Given data:

The mass of planet is, $m_{1}=7.503 \times 10^{24} \;\rm kg$ .

The mass of moon is, $m_{2}=2.703 \times 10^{22} \;\rm kg$ .

The average distance between the centers is, $d = 2.803 \times 10^{8} \;\rm m$ .

(a)

The magnitude of gravitational force between the moon and planet is,

$F = \dfrac{G \times m_{1} \times m_{2}}{d^{2}} \\\\F = \dfrac{6.67 \times 10^{-11} \times 7.503 \times 10^{24} \times 2.703 \times 10^{22}}{(2.803 \times 10^{8})^{2}} \\F =1.721 \times 10^{20} \;\rm N$

Thus, the magnitude of gravitational force between the moon and planet is $1.721 \times 10^{20} \;\rm N$ .

(b)

The acceleration of moon towards the planet is obtained as,

$F = m_{2} \times a\\1.721 \times 10^{20} = 2.703 \times 10^{22} \times a\\a = 6.36 \times 10^{-3} \;\rm m/s^{2}$

Thus, the acceleration of moon towards the planet is $6.36 \times 10^{-3} \;\rm m/s^{2}$ .

(c)

Now, the acceleration of planet towards the moon is obtained as

$F = m_{1} \times a'\\1.721 \times 10^{20} = 7.503 \times 10^{24} \times a'\\a' = 2.29 \times 10^{-5} \;\rm m/s^{2}$

Thus, the acceleration of planet towards the moon is $2.29 \times 10^{-5} \;\rm m/s^{2}$ .

Learn more about the gravitational force here:

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Answer from: Quest

a coal burning power plant

Answer from: Quest

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.

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(a) find the magnitude of the gravitational force between a planet with mass 7.50 3 1024 kg and its...