Two objects attract each other with a gravitational force of 25 newtons from a given distance. If the distance between the two objects is reduced by a factor of 5, what is the changed force of attraction between them?
since gravity is an inverse square law,
multiplying the distance by 1/5, multiplies the force by a factor of (1/(1/5))^2 or 5^2
So the force changes to 25*5^2 = 625 N
To find the changed force of attraction between two objects when the distance is reduced by a factor of 5, we need to use the inverse square law of gravitation.
The gravitational force between two objects is given by the equation:
F = G * (m1 * m2) / r^2
Where:
F is the force of attraction between the two objects,
G is the gravitational constant,
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of mass of the two objects.
In this case, we know that the force of attraction is 25 newtons at the given distance.
Let's assume that the distance between the objects is d. When the distance is reduced by a factor of 5, the new distance becomes d/5.
Now, we can set-up the equation for the changed force of attraction:
F' = G * (m1 * m2) / (d/5)^2
To find the changed force, we need to figure out the ratio of the new force to the original force.
F' / F = [G * (m1 * m2) / (d/5)^2] / 25
Simplifying,
F' / F = 5^2 / 1
F' / F = 25
Therefore, the changed force of attraction between the two objects, when the distance is reduced by a factor of 5, is also 25 newtons.
The force of attraction between two objects is inversely proportional to the square of the distance between them.
Let's assume the original distance between the two objects is 'd'. The original force of attraction between them is 25 newtons.
If the distance is reduced by a factor of 5, the new distance between the objects becomes 'd/5'.
According to the inverse square law, the new force of attraction between the objects can be calculated as:
(New Force) = (Original Force) * (Original Distance^2 / New Distance^2)
Plugging in the given values:
(New Force) = 25 * (d^2 / (d/5)^2)
Simplifying the expression, we get:
(New Force) = 25 * (d^2 / (d^2 / 25))
(New Force) = 25 * (25 / 1)
So, the changed force of attraction between the objects is 625 newtons.