QUIZ 6

1. A taught massless string passes over a massless and frictionless pulley and connects two blocks of masses m₁ = 5kg, m₂ = 2kg, which are originally at rest as shown in the figure. The block m₁ rests on the table; the coefficient of friction between m₁ and the table is 0.25. Find the speed of m₁ after it moves 3m on the table. Use conservation of energy to solve this problem.

Solution. We choose y = 0 at the table level. Use conservation of energy we have DE = WNC.                Ei = 0.                Ef = Ek + PE = 1/2(m1 + m2)v + m2gy; The only non-conservative force is the friction force, Ffr = mkFN = mkm1g. Thus we have               Ffrx = Ef  -  Ei = 1/2(m1 + m2)v + m2gy - 0;               mkm1gx = 1/2(m1 + m2)v2 + m2gy;              (0.25)(5kg)(9.80m/s2)(3m) = 1/2(5kg + 2kg)v2 + (2kg)(9.80m/s2)(-3m), which gives v = 5.22m/s.

2. A 150-hp car runs at 60km/h. Find the average force the engine exerts on the car.

Solution. We find the force from

              P = Fv;

             (150hp)(746W/hp) = F(60km/h)(1000m/km)/(3.6ks/h), which gives F = 6.7 x 10³N.