Final answer:
To find potential energy in pounds and miles, the mass and height need to be converted into metric units before using the formula PE = mgh. Calculating the potential energy of a car driving up a mountain also requires considering factors that affect energy efficiency, such as mechanical losses and aerodynamic drag.
Step-by-step explanation:
To find the potential energy of an object in pounds and miles, you can use the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height above the reference point. Potential energy is the energy that is stored in an object due to its position in a force field, commonly gravitational. When working with imperial units such as pounds and miles, you may need to convert them to the standard metric units to apply the formula correctly, as gravitational acceleration (g = 9.81 m/s²) is given in metric units. However, in practice, calculations can also be modified to work directly with imperial units with the appropriate conversion factors.
For example, to calculate the potential energy of a 1360 kg automobile (which is approximately 3000 pounds) parked on the top level of a parking garage 36.6 m (120 ft) high, you would plug these values into the formula as follows: PE = (1360 kg)(9.81 m/s²)(36.6 m) to find the energy in joules. If you were given the mass in pounds and the height in miles, you would need to convert pounds to kilograms (1 pound is approximately 0.453592 kg) and miles to meters (1 mile is approximately 1609.34 meters) before performing the calculation.
In terms of car efficiency on a trip like driving up Pike's Peak, factors that may reduce efficiency include mechanical losses in the engine and drivetrain, aerodynamic drag, rolling resistance, changes in kinetic energy, and the energy required to overcome the incline, as not all of the fuel's energy is converted into gravitational potential energy. It's also vital to compare the actual energy consumption to the thermodynamic efficiency quoted for gasoline engines, which accounts for the ideal maximum percentage of fuel energy that can be converted into work.