Question

A gallon of gasoline contains about 1.3 x 108joules

of energy. A 2000 kg car traveling at 20 m/s skids to astop.
Estimate how much gasoline it will take to bring the car backto the
original speed? To complicate matters further, consider thefact
that only about 15% of the energy extracted from gasolineactually
propels the car. The rest gets exhausted as heat andunburnt
fuel.

Answer 1

The amount of gasoline is
`2.105*10^(-2)\ gallons`.

Step-by-step explanation:

Given that,

Energy contained in gasoline
`= 1.3*10^(8)\ J`

Mass = 2000 kg

Speed = 20 m/s

Energy used propel the car
`E=15\%\ of 1.3*10^(8)\ J`

`E=(15)/(100)*1.3*10^(8)`

`E=19500000 = 1.9*10^(7)\ J`

`E=1.9*10^(7)\ J`

We need to calculate the work done by the frictional force to stop the car

Using formula of work done

`W=\Delta KE`

`W=(1)/(2)m(v_(f)^2-v_(0)^2)`

`W=(1)/(2)*2000*(0-20^2)`

`W=-4.0*10^(5)\ J`

Therefore,

Work done to bring the car back to its original speed

`W=4.0*10^(5)\ J`

`Amount\ of\ gasoline\ needed = (W)/(E)`

`Amount\ of\ gasoline =(4.0*10^(5))/(1.9*10^(7))`

`Amount\ of\ gasoline =2.105*10^(-2)\ gallons`

Hence, The amount of gasoline is
`2.105*10^(-2)\ gallons`.