Physics, 07.04.2020 16:24 anggar20

Two objects, with masses m1 and m2 , are originally a distance r apart. The magnitude of the gravitational between is F. The masses are changed to 2m1 and 2m2 , and the distance is changed to 4r. What is the magnitude of the new gravitational force?

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Answer from: lllamasarebae3061

According to Newton's gravitational law, the magnitude of the gravitational force is:

$F=-G\frac{m_1m_2}{r^2}$

In this case, we have: m_1'=2m_1,m_2'=2m_2, r'=4r

Therefore, replacing this values and solving for F' in function of F:

$F'=-G\frac{m_1'm_2'}{r'^2}\\F'=-G\frac{2m_1(2m_2)}{(4r)^2}\\F'=-G\frac{4m_1m_2}{16r^2}\\F'=\frac{1}{4}(-G\frac{m_1m_2}{r^2})\\F'=\frac{1}{4}F$

Answer from: cherryice68

$\frac{1}{4}$ F

Explanation:

Newton's law of gravitation states that the force, F, that exists between the two objects of masses m₁ and m₂ is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance, r, between the bodies. i.e

F ∝ (m₁m₂ / r²)

F = Gm₁m₂/r² ------------------(i)

Where;

G = proportionality constant called the gravitational constant.

Now, when the masses are changed to 2m₁ and 2m₂, and the distance is changed to 4r, then according to equation (i) the new force (say F₂) becomes;

F₂ = G (2m₁)(2m₂) / (4r)²

F₂ = 4Gm₁m₂ / 16r²

F₂ = Gm₁m₂ / 4r²

F₂ = $\frac{1}{4}$ Gm₁m₂/r² -------------------------(ii)

Comparing equations (i) and (ii), equation (ii) can be re-written as;

F₂ = $\frac{1}{4}$ F

Therefore, the magnitude of the new gravitational force is a quarter of the old gravitational force, F. i.e $\frac{1}{4}$ F

Answer from: Quest

newton's first law of motion

Answer from: Quest

Is a vector quantity that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.

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Two objects, with masses m1 and m2 , are originally a distance r apart. The magnitude of the gravita...