QUIZ 3

1. A cart loaded with bricks has a total mass of 18.0kg and is pulled at constant speed by a rope. The rope is inclined at 20.0° above the horizontal, and the cart moves 20.0m on a horizontal surface. The coefficient of kinetic friction between ground and cart is 0.500. (a) What is the tension in the rope? (b) How much work is done on the cart by the rope?

Solution. (a) Since v = constant, a = 0                We have SF  = ma.                 x-component: FTcosq -Ffr = 0   (1)                 y-component: F + Fsinq - mg = 0  (2)                we have Ffr = mkFN = mk(mg - FTsinq)  (3)                Substituting (3) into (1), we get                    FT = (mkmg)/(cosq + mksinq) =(0.500)(18.0kg)(9.80m/s)/[cos20.0° + (0.500)sin20.0°]                       = 79.4N.                 (b) WFT = FTscosq = (79.4N)(20.0m)cos20.0° = 14.9kJ

2. A 700-N marine in basic training climbs a 10.0-m vertical rope at a constant speed in 8.00s. What is his power output?

    Solution. The marine must exert a 700N upward force opposite the force of gravity to lift his body at constant speed. Then his muscles do work:

                              W = F× s = (700Nj )×(10.0mj) = 7000J

                  The power he puts out is

                              P =  W/t = (7000J)/(8.00s) = 875W.