The mileage for a motorcycle with a fuel tank capacity of 22 liters is 35 miles per gallon. The density of gasoline is 0.74 g/cm^3.(dimensional analysis problem)
a). How long a trip, in KM can be made on a full tank of gasoline?
b). if the price of gasoline is $1.99 per gallon, what would the gasoline for the trip be?
c). if the average speed during the trip is 44 miles per hour, how many hours will the trip take?
d). What is the mass, in grams of the fuel in the tank?
a. I would convert 35 mpg to km/L. I obtained 14.88 km/L but you should confirm that.
Then distance = km/L x 22 L = ?
b. 1 gallon = 3.785 L.
$1.99/gallon x (1 gallon/3.785 L) x 22 L = ?
c. Take the km from part a, convert to miles, then
44 mi/hr x #hr = total miles
Solve for # hr.
d. mass = volume x density
volume = 22 L = 22,400 mL
You have the density.
Calculate mass in grams.
a) To calculate the distance in kilometers that can be made on a full tank of gasoline, we need to convert the fuel tank capacity from liters to gallons and then use the given mileage.
First, we convert the fuel tank capacity from liters to gallons:
1 gallon = 3.78541 liters (conversion factor)
22 liters = 22 liters * (1 gallon / 3.78541 liters) = 5.812 gallons
Now, we can calculate the distance in miles that can be traveled on a full tank of gasoline:
Miles = Fuel tank capacity (gallons) * Mileage
Miles = 5.812 gallons * 35 miles/gallon = 203.42 miles
To convert the distance from miles to kilometers, we multiply by the conversion factor:
1 mile = 1.60934 kilometers
203.42 miles = 203.42 miles * (1.60934 kilometers / 1 mile) = 327.49 kilometers
Therefore, a trip of approximately 327.49 kilometers can be made on a full tank of gasoline.
b) To calculate the cost of the gasoline for the trip, we need to multiply the fuel tank capacity in gallons by the price per gallon:
Cost = Fuel tank capacity (gallons) * Price per gallon
Cost = 5.812 gallons * $1.99/gallon = $11.54
Therefore, the cost of gasoline for the trip would be approximately $11.54.
c) To calculate the time the trip will take, we need to divide the distance by the average speed:
Time = Distance / Average speed
Time = 203.42 miles / 44 miles/hour = 4.625 hours
Therefore, the trip will take approximately 4.625 hours.
d) To calculate the mass of the fuel in the tank, we need to multiply the fuel tank capacity in liters by the density of gasoline in grams per cubic centimeter:
Mass = Fuel tank capacity (liters) * Density of gasoline (grams/cm^3)
Mass = 22 liters * (0.74 grams/cm^3) = 16.28 grams/cm^3
Therefore, the mass of the fuel in the tank would be approximately 16.28 grams.
a). First, we need to convert the fuel tank capacity from liters to gallons. Since 1 gallon is approximately equal to 3.785 liters, we can calculate:
Fuel tank capacity in gallons = 22 liters / 3.785 liters/gallon
Fuel tank capacity in gallons = 5.82 gallons
Next, we can calculate the total distance the motorcycle can travel on a full tank of gasoline by multiplying the fuel tank capacity in gallons by the mileage:
Distance on a full tank = Fuel tank capacity in gallons * Mileage
Distance on a full tank = 5.82 gallons * 35 miles/gallon
Now, we convert the distance from miles to kilometers since the question asks for the trip length in kilometers. Since 1 mile is approximately equal to 1.609 kilometers, we can calculate:
Distance on a full tank in kilometers = Distance on a full tank * 1.609 kilometers/mile
b). To calculate the cost of gasoline for the trip, we multiply the distance traveled in miles by the cost per gallon of gasoline:
Gasoline cost = Distance on a full tank * Gasoline price per gallon
c). To calculate the trip duration, we divide the distance traveled in miles by the average speed in miles/hour:
Trip duration = Distance on a full tank / Average speed
d). To calculate the mass of the fuel in the tank, we need to multiply the fuel tank capacity in liters by the density of gasoline:
Mass of fuel in the tank = Fuel tank capacity in liters * Density of gasoline converted to grams
Now let's calculate each of these step-by-step: