PHYSICS 100A QUIZ 2

FALL 2001 #85013

1. (a) Sketch and (b) use vector components to calculate the sum of the vectors as shown in Fig. 1.

Solution (b) We resolve the vectors in components:

       x-component: Rx = Ax + Bx + Cx

                                = (5.0)cos30° - (3.0) + 0 = 1.33

      y-component: Ry = Ay + By + Cy 

                               = (5.0)sin30° + 0 - (4.0) = -1.5

      We find the magnitude of the resultant vector from

                            R = (Rx2 + Ry2)1/2 = [(1.33)2 + (-1.5)2]1/2 = 2.0

      We find the direction of the resultant vector from

                            tan q = (-1.5)/(1.33) = -1.128, which gives q = - 48.4° ( below +x-axis).

 (a)

2. Two forces exert on the 2.5-kg block as shown in figure. How does the block move? What is the acceleration of the block?

 Solution. We write SF = ma

                        F1  -  F2 = ma

                       5N - 3N = (2.5kg)a , which gives a = 0.8m/s2.

                Because F1 > F2,  the net force on the block is to the left (direction of F1 ), the block moves to the left.