SPRING 2002 QUIZ 2

PHYSICS 100A 

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

Solution.

(a)

 

 (b) We resolve the vectors in components:

            x-component: Rx = Ax + Bx + Cx

                                                     = 3.0 + 0 + (6.0)cos60°

                                        = 0.

            y-component:  Ry = Ay + By + Cy

                                        = 0 + 4.0 - (6.0)sin60°

                                        = -1.12 (units)

             Because the x-component of the resultant vector is zero we have

                                    R = -1.12 (units)j

            

 

2. Two forces exert on the 5.0-kg block as shown in Fig. 2. What is the horizontal acceleration of the block?

Solution.

 

 We choose the coordinate system as shown. We write SF = ma

                 x-component: SFx = Fcos20° - Ffr = max;

                                        (15N)cos20° - (2.5N) = (5.0kg)ax,

which gives              ax = 2.32m/s2.