Sorry to repost this, again, but I still don't understand.
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...
Physics Urgent!! - bobpursley, Saturday, April 30, 2011 at 3:31pm
Double the force: you have two big ones, each pulling on one small
Sorry to repost this again but I'm still not clear... 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 part A?
Physics Urgent!!!!! - bobpursley, Saturday, April 30, 2011 at 8:30pm
I didn't punch it on the calculator. OK, on A) it asks (I think) for each force, do don't multipy by 2 .
But, I just have to plug in one number for part A that must be E-7 and for part B I have to plug only one number too that must be E-8... Is my equation right?? If I multiply the answer by two, I still don't get the answer to E-8.
To solve part A, you need to calculate the force of attraction between the larger and smaller balls. You have correctly converted the values to kilograms and meters.
Using the equation F(r) = Gm1m2/r^2, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them, you can calculate the force of attraction.
The mass of the small ball is 0.730283 kg and the mass of the large ball is 157.850 kg. The distance between them, r, is given as the difference between the radii: r = (0.152 m - 0.0254 m).
Substituting these values into the equation, you should get:
F(r) = (6.674E-11 m^3 kg^-1 s^-2) * (0.730283 kg) * (157.850 kg) / (0.152 m - 0.0254 m)^2
Calculating the expression in the brackets:
r = 0.1266 m
Substituting this value into the equation:
F(r) = (6.674E-11 m^3 kg^-1 s^-2) * (0.730283 kg) * (157.850 kg) / (0.1266 m)^2
Solving this expression should give you the force of attraction between the balls.
For part B, you are asked to compare this force to the weight of the small balls. The weight of the small balls can be calculated using the formula W = mg, where W is weight, m is mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The weight of the small balls is:
W = (0.730283 kg) * (9.8 m/s^2)
Comparing the force of attraction from part A to the weight of the small balls, you can determine if they are equal, greater, or smaller.
I hope this helps!