Energy to a 40% efficient engine

[laxmanic33]

Homework Statement

A 40%-efficient car engine accelerates the 1200 kg car from rest to 18 m/s.
How much energy is transferred to the engine by burning gasoline?

any help is appreciated

 

[cepheid]

1. How much work is done by the engine?
2. Is all of the engine's energy being used to do that work? No, because the engine is not 100% efficient.
3. So how much energy must be released by burning in order for the engine to be able to do the amount of work calculated in (1) after 60% of said energy is thrown away?

 

[thomate1]

I can provide a response to this content by using the principles of thermodynamics and energy conservation. First, we need to understand that the efficiency of an engine is the ratio of the useful work output to the total energy input. In this case, the 40% efficiency of the engine means that 40% of the energy from burning gasoline is converted into useful work to accelerate the car.

To calculate the energy transferred to the engine, we need to use the equation for kinetic energy, which is 1/2 * mass * velocity^2. In this case, the mass of the car is given as 1200 kg and the final velocity is 18 m/s. Therefore, the kinetic energy of the car is 1/2 * 1200 kg * (18 m/s)^2 = 194,400 J.

Since the engine is 40% efficient, we can calculate the total energy input as the kinetic energy divided by the efficiency. So, the energy transferred to the engine is 194,400 J / 0.4 = 486,000 J.

Therefore, the amount of energy transferred to the engine by burning gasoline is 486,000 J. This energy is then converted into useful work to accelerate the car.