Physics, 25.12.2019 19:31, jstamey757

(ii) two objects attract each other gravitationally with a force of 2.5 × 10 ^–10 n when they are 0.25 m apart. their total mass is 4.00 kg. find their individual masses.

Answers: 2

Show answers

Answers

answered: Zaxx2974

The individual masses of the two objects are 0,06 kg and 3,94 kg.

Explanation:

To solve this we need to use Newton's law of universal gravitation that states that the force of gravity between two massive bodies 1 and 2, is proportional to their masses M₁ and M₂ and inversely proportional to the square of the distance d that separates them:

$F=\frac{G M_{1}M_{2}}{d^{2} }$

with $G=6,67 x 10^{-11} \frac{Nm^{2} }{kg^{2} }$ being the universal gravitational constant.

We are told:

the value of F when it says that the objects attract each other gravitationally with a force of $2.5x10^{-10}N$ ,the value of d when it says that they are 0.25 m apart.

When it says that their total mass is 4.00 kg it means that:

$M_{1} +M_{2} =4.00\ kg$

$M_{2} =4.00\ kg-M_{1}$

replacing all of this in the original equation $F=\frac{G M_{1}M_{2}}{d^{2} }$ we get

$2.5x10^{-10}N=6.67x10^{-11}\frac{Nm^{2}}{kg^{2}} \frac{M_{1}(4.00kg-M_{1})}{(0.25)^{2}m^{2}}$

$2.5x10^{-10}N=\frac{6.67x10^{-11}Nm^{2}}{(0.25)^{2}m^{2}kg^{2}}(M_{1}4.00kg-M_{1} ^{2})$

$2.5x10^{-10}N=\frac{6.67x10^{-11}N}{(0.25)^{2}kg^{2}}(M_{1}4.00kg-M_{1} ^{2})$

$\frac{2.5x10^{-10} }{6.67x10^{-11}}(0.25)^{2}kg^{2}=4.00kg\ M_{1}-M_{1} ^{2}$

if we put all terms in one side we get

$M_{1} ^{2} -4.00kg\ M_{1} +\frac{2.5x10^{-10}}{6.67x10^{-11}}(0.25)^{2}kg^{2} =0$

$M_{1} ^{2} -4.00kg\ M_{1} +0.23\ kg^{2} =0$

we have to solve a quadratic equation $ax^{2} +bx+c=0$ where a=1, b=-4.00 and c=0.23. Here x=M₁.

We replace these values in the quadratic formula for the roots:

$x=\frac{-b+-\sqrt{b^{2}-4.a.c}}{2a}$

so we get

$x=\frac{4.00+-\sqrt{16-4.1.0.23}}{2}$

$x=\frac{4.00+-\sqrt{16-0.92}}{2}$

$x=\frac{4.00+-\sqrt{15.08}}{2}$

$x=\frac{4.00+-3.88}{2}$

the possible roots are

$x_{1} =\frac{4.00+3.88}{2}=\frac{7.88}{2}=3.94$

$x_{2} =\frac{4.00-3.88}{2}=\frac{0.12}{2}=0.06$

given that M₁+M₂=4.00 kg the possible values of M₂ are then

$M_{2}=4.00kg-3.94kg=0.06kg$

$M_{2}=4.00kg-0.06kg=3.94kg$

Either one of the individual masses M₁ and M₂ could be 0.06 kg or 3.94 kg.

answered: Guest

specific latent heat of fusion, lf, of a substance is defined as the amount of heat required to change a unit mass of the substance from solid to liquid state, without any change in the temperature.

explanation:

answered: Guest

"i have always loved contemporary art and made it a general goal to work within the field. after a few nonprofit internships at museums and galleries, i decided to try the for-profit art world and was offered a job as the ad assistant at the magazine. i much prefer the pace of the for-profit art community and have stayed with the company for three years, with a promotion to an account manager last spring."

i just did this and got a 100.

Other questions on the subject: Physics

Physics, 22.06.2019 01:00, jayycruz59

An object is 10. cm from the mirror, its height is 3.0 cm, and the focal length is 2.0 cm. what is the image height? (indicate the object orientation by including the + or - sign with the answer.) hi = cm +1.33 -1.33 +0.75 -0.75

Answers: 2

continue

Physics, 22.06.2019 10:00, ceasar6071

Students design a model roller-coaster track. they place a rubber ball at the highest point on the track and let it go. the ball rolls along the track pulled only by the force of gravity. eventually, it comes to a stop. which change to the design will result in the ball moving the greatest distance?

Answers: 1

continue

Physics, 22.06.2019 11:00, zhjzjzzj6325

Afisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. it takes a time of 2.20 s for the boat to travel from its highest point to its lowest, a total distance of 0.670 m . the fisherman sees that the wave crests are spaced a horizontal distance of 5.80 m apart. (a) how much is the wavelength? (b) find the period of the wave. (c) how fast are the waves traveling? (d) what is the amplitude a of each wave?

Answers: 3

continue

Physics, 22.06.2019 16:10, estefaniapenalo

To a of 4 x hz is 1. 0. mm nm nm

Answers: 1

continue

Do you know the correct answer?

(ii) two objects attract each other gravitationally with a force of 2.5 × 10 ^–10 n when they are 0....