question_answer 73)

                  On complete combustion a litre of petrol gives off heat equivalent to \[3\times {{10}^{7}}\,J\] . In a test drive, a car weighing 1200 kg including the mass of driver, runs 15 kin per litre while moving with a uniform speed on a straight track. Assuming that friction offered by the road surface and air to be uniform, calculate the force of friction acting on the car during the test drive, if the efficiency of the car engine were 0.5.                

Answer:

                  Total energy \[=3\times {{10}^{7}}\,J\]                 Efficiency of car engine = 0.5                 \ Output or energy used to drive car                 \[=\text{efficiency }\times 3\times {{10}^{7}}J=0.5\times 3\times {{10}^{7}}J\]             \[=1.5\times {{10}^{7}}J\]                 Thus, energy used to drive car by the combustion of 1 litre petrol \[=1.5\times {{10}^{7}}J\]                 Work done = energy used                 If F = force of friction acting on the car                 Then \[F\times S=1.5\times {{10}^{7}}\]                 \[F=\frac{1.5\,\times \,{{10}^{7}}}{S}\,\,=\,\frac{1.5\times {{10}^{7}}}{15\,\times {{10}^{3}}}\]                                                                 \[(\because \,\,S=15km)\]                 \[={{10}^{3}}N.\]