100A QUIZ 3

1. A man pushes a shopping-cart with a 2.5-N force with an angle of 35º to the horizontal as shown in the figure. The friction force between the cart and the ground is 0.85N. The cart moves 16m horizontally. Find the net work done to the cart.

Solution. We draw the free-body diagram of the cart as shown.                Because the cart moves horizontally with constant speed. Only the horizontal forces do work to the cart.                We choose the coordinate system as  shown. We write the net  horizontal force as                             Fx = Fcos q - Ffrcos180° = (2.5N)cos35° + (0.85N)cos180                                   = 1.198N               We get the net work                            Wnet = Fxd = (1.198N)(16m) = 19.17J.

2. A block slides down along a 10-m incline with the height of 2m. Use conservation of energy to find the block’s speed when it reaches the bottom of the incline. Neglect the friction between the block and the incline.

Solution. According to conservation of mechanical energy we have

                                   KE + PE = constant.

              When the block is on the top of the incline we have

                                   KE = 0, PE = mgh

              When the block reached the bottom of the incline  we have

                                   KE = 1/2mv²;  PE = 0.

              Thus we have

                                  0 +  mgh  = 1/2mv² + 0;

                                  0 + m(9.80m/s²)(2m) = 1/2mv² + 0, which gives v = 6.26m/s.