A family in Charlotte wants to drive to a campsite next to Mt. Mitchell. Their trip will take them 2km up in elevation. They have the choice of taking their top-of-the-line Tesla model S P100D, which when fully charged has 100 kWh of stored energy in the batteries (and for this problem is 100% efficient at converting its stored energy into kinetic energy) and a mass of 2200kg, or their choice of taking their 2021 Ford F-150. Gasoline has an energy density of 34.2 Megajoules per liter. The family owns the smallest 2021 Ford F-150, and so it has a fuel tank of 23 gallons. Assume the F-150’s engine is able to convert 30% of the energy stored in its gasoline tank into kinetic energy (typical efficiency for gasoline engines), with the rest of the stored energy in the gasoline lost to heat. The mass of this model F-150 is about 2000kg. They are going to tow their big pop-up trailer to the campsite. For this question, assume that each vehicle must use a combined 79 kWh of energy to combat the wind resistance of moving at 75 mph with the trailer for the whole drive, and to combat the rolling resistance of the tires for the long journey up the mountains to the campsite; and another 79 kWh for the drive down the mountains back to Charlotte. Assume you cannot charge the Tesla at the top of the mountain, and assume the mass of the trailer is incorporated into the 79 kWh figure it takes (i.e. you don't have to solve for the potential energy of the trailer going up and down, you can just ignore that piece and assume it is already solved for you with the 79 kWh figure) 1. How many kWh of energy is left in the Tesla’s battery when it gets to the campsite? 2. How many kWh of effective useable energy is left in the Ford’s gas tank when it gets to the campsite? (By effective useable I mean considering only the energy the engine can take out of the gas, and neglecting all the energy that will be lost to heat in the entire tank...so like, subtract out the energy that will be lost to heat if the whole tank of gas was used) 3. Can the Tesla make it to the campsite and back home on one full charge?
A family in Charlotte wants to drive to a campsite next to Mt. Mitchell. Their trip will take them 2km up in elevation. They have the choice of taking their top-of-the-line Tesla model S P100D, which when fully charged has 100 kWh of stored energy in the batteries (and for this problem is 100% efficient at converting its stored energy into kinetic energy) and a mass of 2200kg, or their choice of taking their 2021 Ford F-150. Gasoline has an energy density of 34.2 Megajoules per liter. The family owns the smallest 2021 Ford F-150, and so it has a fuel tank of 23 gallons. Assume the F-150’s engine is able to convert 30% of the energy stored in its gasoline tank into kinetic energy (typical efficiency for gasoline engines), with the rest of the stored energy in the gasoline lost to heat. The mass of this model F-150 is about 2000kg. They are going to tow their big pop-up trailer to the campsite.
For this question, assume that each vehicle must use a combined 79 kWh of energy to combat the wind resistance of moving at 75 mph with the trailer for the whole drive, and to combat the rolling resistance of the tires for the long journey up the mountains to the campsite; and another 79 kWh for the drive down the mountains back to Charlotte.
Assume you cannot charge the Tesla at the top of the mountain, and assume the mass of the trailer is incorporated into the 79 kWh figure it takes (i.e. you don't have to solve for the potential energy of the trailer going up and down, you can just ignore that piece and assume it is already solved for you with the 79 kWh figure)
1. How many kWh of energy is left in the Tesla’s battery when it gets to the campsite?
2. How many kWh of effective useable energy is left in the Ford’s gas tank when it gets to the campsite? (By effective useable I mean considering only the energy the engine can take out of the gas, and neglecting all the energy that will be lost to heat in the entire tank...so like, subtract out the energy that will be lost to heat if the whole tank of gas was used)
3. Can the Tesla make it to the campsite and back home on one full charge?
4. If so, how many kWh are left in its batteries when it gets home?
5. Can the Ford make it to the campsite and back home on one full tank?
6. If so, how many kWh are left in its fuel tank when it gets home?
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