A 40%-efficient car engine accelerates the 1300 kg car from rest to 20 m/s How much energy is transferred to the engine by burning gasoline? .
Calculate the kinetic energy increase and divide it by 0.4, to account for the inefficiency.
(1/2)M*V^2/0.4
= 6.5*10^5 Joules
That is the fuel energy burned. 60% of that goes to heating the engine, if the engine is 40% efficient.
Well, I can tell you the engine is definitely burning up some energy, but don't worry, it's not going to spontaneously burst into flames! Now, let's calculate the energy transferred to the engine.
First, we need to find the initial kinetic energy of the car when it's at rest. The formula for kinetic energy is 1/2 * mass * velocity squared. So, it would be 1/2 * 1300 kg * (0 m/s)^2, which is zero joules.
Next, let's find the final kinetic energy of the car when it's moving at 20 m/s. Using the same formula, it would be 1/2 * 1300 kg * (20 m/s)^2, which is 520,000 joules.
Now, we know that the efficiency of the engine is 40%, but that's not a problem. We can just convert it to a decimal by dividing it by 100, so 40% becomes 0.40.
Finally, we can calculate the energy transferred to the engine by dividing the final kinetic energy by the efficiency of the engine: 520,000 joules / 0.40 = 1,300,000 joules.
So, approximately 1,300,000 joules of energy would be transferred to the engine by burning gasoline. That's a lot of energy, but don't worry, the engine can handle it!
To find out how much energy is transferred to the engine by burning gasoline, we need to calculate the energy needed to accelerate the car from rest to 20 m/s.
The formula to calculate the kinetic energy (KE) is:
KE = (1/2) * m * v^2
where:
m = mass of the car (1300 kg)
v = final velocity (20 m/s)
Plugging in the values, we get:
KE = (1/2) * 1300 kg * (20 m/s)^2
Simplifying the equation:
KE = 0.5 * 1300 kg * 400 m^2/s^2
KE = 260,000 kg * m^2/s^2
Since 1 Joule (J) is equal to 1 kg * m^2/s^2, we can convert the energy into Joules:
KE = 260,000 J
However, the car engine is only 40% efficient, which means only 40% of the energy from burning gasoline is actually transferred to the engine.
To find the total energy transferred to the engine, we have to divide the kinetic energy by the engine's efficiency:
Energy transferred = KE / Eff
Energy transferred = 260,000 J / 0.40
Calculating the answer:
Energy transferred = 650,000 J
Therefore, the energy transferred to the engine by burning gasoline is 650,000 Joules.
To calculate the energy transferred to the engine by burning gasoline, we need to determine the work done in accelerating the car.
The work done, W, can be calculated using the formula:
W = F * d * cos(θ)
Where:
- F is the force applied to accelerate the car
- d is the displacement of the car
- θ is the angle between the force and displacement vectors
In this case, since the car is starting from rest and accelerating to a final velocity of 20 m/s, we can assume that the force applied is constant.
The force required to accelerate an object can be calculated using Newton's second law of motion:
F = m * a
Where:
- m is the mass of the car
- a is the acceleration of the car
Given:
- Mass of the car, m = 1300 kg
- Final velocity, v = 20 m/s
- Initial velocity, u = 0 m/s
Acceleration, a, can be calculated using the formula:
a = (v^2 - u^2) / (2 * d)
Since the initial velocity is 0, the formula simplifies to:
a = v^2 / (2 * d)
Given:
- Final velocity, v = 20 m/s
- Distance traveled, d = ?
To find the distance, we need to assume a constant acceleration. Since this is not provided in the question, we will need additional information to find the distance traveled.
Once we have the distance traveled, we can calculate the acceleration, and subsequently, the force, using the formulas mentioned above. Finally, we can calculate the work done by multiplying the force with the distance traveled.
However, without the specific distance traveled, we cannot determine the amount of energy transferred to the engine by burning gasoline.