Question

a 10% efficient engine accelerates a 1500 kg car from rest to 15 m/s. how much energy is transferred to the engine by burning gasoline?

Answer 1

Data Given

mass of the car m = 1500 kg, initial velocity v_i = 0 m/s, final velocity v_f = 15 m/s

efficiency $\eta = 10 \%$

Now output is equal to work done and we will calculate work done using work energy theorem.

According to work energy theorem work done = change in kinetic energy

$W = \frac{1}{2}mv_{f}^{2}-\frac{1}{2}mv_{i}^{2}$

$W = \frac{1}{2}\times 1500 kg \times (15 m/s)^{2}- \frac{1}{2}\times 1500 kg \times (0 m/s)^{2}$

$W = 168750 J$

Now we know that efficiency is given by

$\eta = \frac{Output}{Input}\times 100$

So

$\eta = \frac{168750 J}{E_{Input}}\times 100 = \frac{10}{100}\times 100$

$\frac{168750 J}{E_{Input}}= \frac{10}{100}$

$E_{Input}= 168750 J\times \frac{100}{10}= 1687500 J$

Einput = 1687.5 kJ