Newton’s Law of Gravity specifies the magnitude of the interaction force between two point masses, m1 and m2, separated by the distance r as F(r) = Gm1m2/r^2. The gravitational constant G can be determined by directly measuring the interaction force in the late 18th century by the English scientis Henry Cavendish. This apparatus was a torsion balance consisting of a 6.00-ft wooden rod suspended from a torsion wire, with a lead sphere having a diameter of 2.00 in and a weight of 1.61 lb attached to each end. Two 12.0-in, 348-lb lead balls were located near the smaller balls, about 9.00 in away, and held in place with a separate suspension system. Today’s accepted value for G is 6.674E-11 m^3 kg^-1s^-2.

a) Determine the force of attraction between the larger and smaller balls that had to be measured by this balance.
b) Compare this force to the weight of the small balls.

Ok... so for the first one I have to use the equation given and change the values to kilograms and meters, and use the radii instead of the diameters, this is what I know, but I don't know how to do it when there are three spheres (the big one and the 2 small ones)... I don't get what they are asking for the second part...

Someone please help, it will be deeply appreciated...

Double the force: you have two big ones, each pulling on one small

Ok, so I have r1= 0.0254m, m1=0.730283 kg, r2= 0.152m and m2=157.850 kg... I calculated

(6.674E-11)(0.730283)(157.850)/(0.152m-0.0254m)^2 and I got 4.77E-7 and multiplyed it by 2 and then I got 9.54 E-7... Does this looks right?

Is that for A?

To determine the force of attraction between the larger and smaller balls, you can use the formula given in Newton's Law of Gravity: F(r) = Gm1m2/r^2. Here, m1 and m2 are the masses of the two objects, and r is the distance between their centers.

Let's break down the problem step by step:

a) To find the force of attraction between the larger and smaller balls, we need to calculate the values for mass (m1 and m2), as well as the distance (r) between their centers.

- The smaller ball has a weight of 1.61 lb, so we need to convert its weight to mass. Since weight is the force due to gravity, we can use the conversion factor 1 lb ≈ 0.454 kg. Thus, the mass of each small ball is approximately (1.61 lb) × (0.454 kg/lb) = 0.730 kg.

- The larger balls have weights of 348 lb. Using the same conversion factor, the mass of each large ball is approximately (348 lb) × (0.454 kg/lb) = 158 kg.

- The distance between the centers of the larger and smaller balls is given as 9.00 inches, which is equivalent to 0.2286 meters.

Now that we have the values for mass (m1 = m2 = 0.730 kg) and distance (r = 0.2286 meters), we can substitute them into the formula:

F(r) = Gm1m2 / r^2

Using the value for G given (G = 6.674E-11 m^3 kg^-1 s^-2), we can calculate the force of attraction between the balls.

b) The second part of the question asks you to compare the force of attraction between the larger and smaller balls to the weight of the small balls.

To find the weight of the small balls, we can simply multiply their mass (0.730 kg) by the acceleration due to gravity (g = 9.8 m/s^2):

Weight of small balls = mass × acceleration due to gravity
= 0.730 kg × 9.8 m/s^2

Finally, compare the force of attraction between the balls (calculated in part a) to the weight of the small balls (calculated now).

If you have any further questions, feel free to ask!