(a) What is the magnitude of the momentum of a 10,000-kg truck whose speed is 12.0 m/s? (b) What speed would a 2000-kg SUV have to attain in order to have (i) the same momentum? (ii) the same kinetic energy?
Solution 1E Momentum of a body of mass m and speed v is given by p = mv . The relationship 2 between momentum and kinetic energy is given by p = 2mE . (a) Given that, mass of the truck m = 10,000 kg Speed v = 12.0 m/s Therefore, the momentum of the truck will be p = mv p = 10,000 kg × 12.0 m/s p = 120,000 kg.m/s Therefore, the magnitude of momentum of the truck will be 120,000 kg.m/s. p 2 Kinetic energy of the truck E = 2m E = (120,000) /(2 × 10,000) J = 720,000 J (b) Mass of the SUV = 2000 kg 120,000 So, the speed of the SUV to attain the same momentum will be = 2000 m/s = 60 m/s Kinetic energy E = 720,000 J Let the speed of the suv to attain the above kinetic energy is E = 720,000 J is v . s 1 2 Therefore, 2 × 2000 × v s = 720,000 vs 2 = 1440,000m /s 2 2000 2 2 2 vs = 720 m /s vs= 26.8 m/s The SUV should have a speed of 26.8 m/s to get the same kinetic energy.