SPRING 2002 QUIZ 3

PHYSICS 220A #85077

1. Three particles with masses of m1 = 2kg, m2 = 2kg, and m3 = 4kg are located as shown in the figure. Find the universal gravitational force exerted on m1 by m2 and m3.

Solution.

 

 We choose coordinate system as shown with m1at the origin.

We find the gravitational force on m1 by  m2 from

                  F21 = Gm1m2/r122 j

                              = (6.67 x 10-11N·m2/kg2)(2kg)(2kg)/(1m)2j

                         = 2.68 x 10-10Nj.

We find the gravitational force on m1 by  m3 from

                 F31 = Gm1m3/r132 i

                             = (6.67 x 10-11N·m2/kg2)(2kg)(4kg)/(2m)2i

                        = 1.13 x 10-10Ni

We find the resultant force from

                 F1 = F21 + F31

                       F1 = [(2.68 x 10-10N)2 + (1.13 x 10-10N)2]1/2

                      = 2.91 x 10-10N

We find the direction of the force from

                 tan q = F21/F31 = (2.68 x 10-10N)/(1.13 x 10-10N) = 2.371, 

which gives q = 67.1°

       

 

2. A force F = (10.0x i + 9.0j + 12.0k)N acts on a small object. The small object moves along the x-axis from x1 = 1m to x2 = 3m. Find the work done by the force.

Solution.

We find the work done by the force from

                   W = òx1x2 F·dx

                       = ò1m3m(10.0xi + 9.0j + 12.0k)N·dxi

                       = ò1m3m (10.0xdx)N

                       = 5.0x2|1m3mJ

                       = 40.0J.