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 $15\,km$ 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 $0.5$.
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 $15\,km$ 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 $0.5$.
Petrol gives energy in the form of heat of combustion.
Thus, by question,
$\mathrm{E}_{\text {input }}=3 \times 10^{7} \mathrm{~J}$
$\eta=0.5$
$\therefore \quad \mathrm{E}=0.5 \times 3 \times 10^{7} \mathrm{~J}=1.5 \times 10^{7} \mathrm{~J}$
Total distance travelled $(d)=15 \mathrm{~km}=15 \times 10^{3} \mathrm{~m}$
If $f$ is the force of friction, then
$\mathrm{E}=f \times d \quad(\because$ energy is utilised in working against friction $)$
$1.5 \times 10^{7}=f \times 15 \times 10^{3}$
$f=\frac{1.5 \times 10^{7}}{15 \times 10^{3}}=10^{3} \mathrm{~N}$
$f=1000 \mathrm{~N}$
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