A compact car of mass 900 kg has an overall motor efficiency of 15.0% . (That is, 15% of the ene

A compact car of mass 900 kg has an overall motor efficiency...

A compact car of mass 900 $\mathrm{kg}$ has an overall motor efficiency of 15.0$\%$ . (That is, 15$\%$ of the energy supplied by the fuel is delivered to the wheels of the car.) (a) If burning one gallon of gasoline supplies $1.34 \times 10^{8} \mathrm{J}$ of energy, find the amount of gasoline used in accelerating the car from rest to 55.0 $\mathrm{mi} / \mathrm{h}$ . Here you may ignore the effects of air resistance and rolling friction. (b) How many such accelerations will one gallon provide? (c) The mileage claimed for the car is 38.0 $\mathrm{mi} / \mathrm{gal}$ at 55 $\mathrm{mi} / \mathrm{h}$ . What power is delivered to the wheels (to overcome frictional effects) when the car is driven at this speed?

A compact car of mass 900 $\mathrm{kg}$ has an overall motor efficiency of 15.0$\%$ . (That is, 15$\%$ of the energy supplied by the fuel is delivered to the wheels of the car.) (a) If burning one gallon of gasoline supplies $1.34 \times 10^{8} \mathrm{J}$ of energy, find the amount of gasoline used in accelerating the car from rest to 55.0 $\mathrm{mi} / \mathrm{h}$ . Here you may ignore the effects of air resistance and rolling friction. (b) How many such accelerations will one gallon provide? (c) The mileage claimed for the car is 38.0 $\mathrm{mi} / \mathrm{gal}$ at 55 $\mathrm{mi} / \mathrm{h}$ .
What power is delivered to the wheels (to overcome frictional effects) when the car is driven at this speed?

Key Concepts

Power

Power is defined as the rate at which work is done or energy is transferred over time. In the context of vehicles, it quantifies how quickly energy is being used or delivered by the engine or overcoming frictional forces, which is essential when evaluating performance metrics like speed and fuel consumption.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion. In dynamics, when an object like a car accelerates, its kinetic energy increases according to the formula KE = ½mv². This concept is central to understanding how much energy is required to change the speed of a vehicle from rest to a given velocity.

Work–Energy Principle

The work–energy principle states that the work done on an object is equal to its change in kinetic energy. This principle links the force applied over a distance (work) to the energy gained or lost by an object, and is crucial for analyzing scenarios involving acceleration, where energy is transferred to the vehicle.

Efficiency

Efficiency measures the ratio of useful output energy to the input energy supplied. In problems involving engines and fuel, overall motor efficiency expresses how much of the chemical energy in the fuel is converted into useful work, such as delivering power to the wheels, with the remainder lost as heat and other forms of energy.

Fuel Energy Density

Fuel energy density is the amount of energy stored in a given mass or volume of fuel. It is a critical concept for calculating the total chemical energy available from a fuel source, which can then be related to the mechanical work performed by an engine or vehicle after accounting for efficiency losses.

Fuel Economy

Fuel economy refers to the distance a vehicle can travel per unit volume or mass of fuel, often used as a measure of efficiency in transportation. It relates the energy consumption during motion, including overcoming resistive forces like friction and air resistance, to the actual fuel used, providing a practical measure of a vehicle’s performance and efficiency.

Transcript

00:01 Video i'm going to be looking at the relationship between energy, work, and power.

00:04 We're going to be looking at a car with a mass m of 900 kilograms.

00:11 That for every one gallon of fuel that this car burns, it gets 1 .34 times 10 to the 8 joules of energy.

00:23 And we know that an engine has an efficiency of 15%, which means that 50%.

00:30 15 % of the energy created in the burning of fuel goes to actually powering the car.

00:36 Knowing this information, i want to find how many gallons of gas do we burn when we accelerate the car from rest.

00:44 So from v initial equals zero to a final velocity of v.

00:50 Final equals 55 miles per hour.

00:55 Okay, so i'm going to use the work energy theorem, and that says my work into the six.

01:00 So the work provided to the engine by burning gasoline.

01:06 My work in equals the change in kinetic energy of my objects, in this case the car.

01:13 We know we start with an initial velocity of zero, so we only have our final component, 1 half mv final squared.

01:23 Okay, so the work done by the burning of the gasoline equals how many gallons of gasoline do i have? times how much work do i get out of burning one gallon? and we said that was 1 .34 times 10 to the 8 joules.

01:38 Times my efficiency, 15%.

01:41 So times 0 .15.

01:43 That equals 1⁄2 times my mass, 900 kilograms.

01:50 It's velocity squared.

01:51 That was 55 miles per hour.

01:54 I converted that to meters per second, so times 24 .5 meters per second squared.

02:01 That gives me and my number of gallons equals 0 .0134 gallons.

02:08 So that's how much fuel it takes us to go from 0 to 55 miles per hour.

02:14 Next we want to know how many times we can do this per gallon of gas...