Question

Leaving the distance between the 97 kg and the 548 kg masses fixed, at what distance from the 548 kg mass (other than infinitely remote ones) does the 69.7 kg mass experience a net force of zero?

Answer 1

The net force on the 69.7 kg mass is zero at a distance of approximately 178 cm from the 548 kg mass.

Step-by-step explanation:

The question is asking at what distance from the 548 kg mass does the 69.7 kg mass experience zero net force, while keeping the distance between the 97 kg and 548 kg masses fixed. To find this distance, we can use Newton's law of universal gravitation which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Using this equation, we find that the net force on the 69.7 kg mass will be zero at a distance of approximately 178 cm from the 548 kg mass.

Answer 2

0.70 d

Step-by-step explanation:

m1 = 97 kg

m2 = 548 kg

m = 69.7 kg

Let the distance between m1 and m2 is d .

Let m be placed at a distance s from m2 so that the net force on m is zero.

Force between m1 and m is balanced by force between m and m2

G m1 x m / (d - s)^2 = G m x m2 / s^2

m1 / (d - s )^2 = m2 / s^2

97 / (d - s)^2 = 548 / s^2

(d - s)^2 / s^2 = 97 / 548

(d - s) / s = 0.42

d - s = 0.42 s

d = 1.42 s

s = 0.70 d