Variation

👨🏻‍🏫 學術台數學

Anonymous

2010-10-03 6:35 pm

The 'law of gravity' states that the gravitation force (F units) between two objects
varies directly as the product of their masses (M kg and m kg), and inversely as
the square of the distance ( d m ) between the two objects. If the mass of each
of the two objects increases by 100% and the distance between them decreases
by 50%, how many times will the new gravitational force be as large as the
original?

更新1:

唔明點計到16

更新2:

OK明了..................

回答 (2)

Godfrey

2010-10-03 7:48 pm

✔ 最佳答案

Gravitation force is given by:

F = GMm/d^2

where G is the universal Gravitational constant,
The other variables F, M, n and d have been defined by the user.

New Gravitation force F2 is given by:
F2 = G(2M)(2n)/[(0.5d)^2]
F2 = 4GMm/(0.25d^2)
F2 = 16GMm/d^2
F2 = 16F

The new gravitational force is 16 times as large as the original one.

👍 0 👎 0

ShingMingTony

2010-10-03 7:13 pm

origginal gravity:
g = GMm/d^2

new gravity:
g = G(1+100%)m(1+100%)M/[d^2(1-50%)^2
=16GMm/d^2

so the new gravitational force is 16 times larger than the original one.

👍 0 👎 0

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