Practice 7I: | 1 | 2 | 3 | Go up 

Gravitational Force

1. If the mass of each ball in Sample Problem 7I is .800 kg, at what
distance between the balls will the gravitational force between the
balls have the same magnitude as that in Sample Problem 7I?

Sample Problem 7I: Find the distance between a 0.300 kg billiard ball and a 0.400 kg
billiard ball if the magnitude of the gravitational force is 8.92x10^-11 N

     Here's what you know, m1 = .800 kg , and m2 = .800 kg, and 
     F = 8.92x10^-11 N and G = 6.67 x 10^-11.  Use the formula F = r2Gm1m2/r2

        1.  To find the distance apart in this problem with the magnitude from the sample 
            problem, plug in the magnitude from the sample problem with the new values
            from this problem into the equation F = Gm1m2/r2

        2.  Plug in the vales: 8.92E-11 N = (6.67E-11 * .800 * .800)/r2

        3.  Solve for r to get r = .692 m
     
        (Table of contents)

2. Mars has a mass of about 6.4 x 10^23 kg, and its moon Phobos has a
mass of about 9.6 x 10^15 kg. If the magnitude of the gravitational
force between the two bodies is 4.6 x 10^15 N, how far apart are Mars and
Phobos? 

     Here's what you know, m1 = 6.4 x 10^23 kg , and m2 = 9.6 x 10^15
     kg, and F = 4.6 x 10^15 N and G = 6.67 x 10^-11.  Use the formula F = Gm1m2/r²

          1. You have to find r, so solve the equation for r

          2  ((G * m1*m2)/F) = r²

          3. ((6.67 x 10^-11 * 6.4E23 * 9.6E15)/4.6E15)) = r²

          4. Plug in the values to get r = 9438643.97 m = 9.4 x 10^6 m = 9.4 x 10^3 km

          (Table of contents)

 3. Find the magnitude of the gravitational force a 67.5 kg person
would experience while standing on the surface of each of the following
     planets:

     a) Earth

     Here's what you know, m1 = 67.5 kg , and m2 = 5.98 x 10^24 kg, and
     r = 6.37 x 10^6 m, and G = 6.67 x 10^-11.  Use the formula F = Gm1m2/r2

          1. Plug in the values into the equation to get F = 664 N

          (Table of contents)

     b) Mars

     Here's what you know, m1 = 67.5 kg , and m2 = 6.34 x 10^23 kg, and
     r = 3.43 x 10^6 m, and G = 6.67 x 10^-11.  Use the formula F = Gm1m2/r2

          1. Plug in the values into the equation 

          F = (6.67 E-11* 67.5 * 6.34 E23)/(3.43E6)2

          Solve it in your calculator to get F = 242.6 N

           (Table of contents)

          c) Pluto

     Here's what you know, m1 = 67.5 kg , and m2 = 5 x 10^32 kg, and r =
4 x 10^5 m, and G = 6.67 x 10^-11.  Use the formula F = Gm1m2/r2

          1. Plug in the values into the equation

          F = (6.67 E-11 * 67.5 * 5E32)/ (4E5)2

          Solve it in your calculator to get F = 1 x 10^4 N
          (Table of contents)