This problem gives you some insights into the energy associated with driving a car, as well as about Mount Washington in New Hampshire, which is the tallest mountain in the northeastern US at 6288 feet.

For this problem, use g = 9.80 m/s².

Note that one gallon of gasoline has an energy content of 33.4 kW h (kilowatt hours). You might find this conversion factor to be helpful: 1 kW h = 3.6 10⁶ joules.

A typical gas-powered car is not very efficient. Let's say your car has an efficiency of 26.0%, which means that only 26.0% of the energy available by burning the gas can be converted to do work (most of the rest is wasted as heat). Out on the highway, your car can travel 28.0 miles on one gallon of gas. We will assume height and speed changes are negligible, so the energy used goes to overcoming various resistance forces (air resistance, rolling resistance of the tires, friction in the wheel bearings, etc.). How much work, on average, is done against these resistive forces in traveling 1.00 mile on the highway? Express your answer as a positive number in joules. _______ J

It's possible to drive up Mount Washington on the Auto Road. (You may have seen bumper stickers on cars saying "This car drove up Mt. Washington".) The Auto Road is 7.60 miles long, and the elevation change from start to finish is 1408 m (the finish being 1408 m higher than the start).

In two steps (part (b) and part (c) ) we'll estimate how much gas we'll burn driving up the Auto Road. (And there are clearly issues with this estimation, but it's probably a reasonable approximation.)

First, ignore the elevation change, and determine how many gallons of gas you would burn on the highway to travel 7.60 miles. _______ gallons

Second, calculate the change in gravitational potential energy associated with your car (mass = 1500 kg) driving up the Mt. Washington Auto Road. That energy also has to come from burning gas in your not-very-efficient car engine. Figure out how many gallons of gas is needed just to produce that change in potential energy, and then add that to your answer from part (b) to get a first approximation of the total amount of gas needed to get your car from the bottom to the top of the Auto Road. _______ gallons

What goes up must come down. On the way down the Auto Road you have to dissipate most (if not all) of the drop in gravitational potential energy as heat, and this can be very hard on the brakes in a typical gas-powered car. For someone driving an electric car or a hybrid car, however, much of that energy can be stored as useful energy in the car's battery pack, using the regenerative braking system. Using the same car mass as given above, and using a conversion efficiency of 90.0% for the conversion of gravitational potential energy (to kinetic energy) to electrical energy, determine how much energy, in kW h, can be stored in the battery pack while driving from the top of Mt. Washington to the bottom of the Auto Road.

How much energy can be stored in the electric / hybrid car's battery pack from driving back down the Mount Washington Auto Road? _______ kW h