(a) Assuming that each cubic centimeter of water has a mass of exactly 1 g, find the mass of 3.76 cubic meter of water in kg. (b) Suppose that it takes 10.4 hours to drain a container of 59.1 m^3 of water. What is the “mass flow rate,” in kg/s, of water from the container?
Isn't big to small conversion, multiply, so you multiply by 10^6 not divide
(a) To find the mass of 3.76 cubic meters of water in kilograms:
1 cubic meter = 1000 liters
1 liter = 1000 cubic centimeters (cc)
Therefore, 1 cubic meter = 1000 * 1000 = 1,000,000 cc.
So, the mass of 1 cubic meter of water = 1,000,000 grams = 1000 kilograms.
Therefore, the mass of 3.76 cubic meters of water = 3.76 * 1000 = 3760 kilograms.
Hence, the mass of 3.76 cubic meters of water is 3760 kilograms.
(b) To find the mass flow rate, we need to divide the total mass of water by the time it takes to drain the container.
Mass flow rate = Mass of water / Time
We already know the mass of the water is 59.1 cubic meters.
To convert hours to seconds, we know that 1 hour = 3600 seconds.
So, time = 10.4 hours * 3600 seconds/hour = 37,440 seconds.
Therefore, the mass flow rate = 59.1 cubic meters / 37,440 seconds = 0.00157813 cubic meters per second.
Now, to convert cubic meters to kilograms, we multiply by the conversion factor we found earlier.
Mass flow rate = 0.00157813 cubic meters/second * 1000 kilograms/cubic meter = 1.57813 kilograms per second.
Hence, the mass flow rate of water from the container is 1.57813 kilograms per second.
To solve these problems, we need to use the given information and make some conversions.
(a) To find the mass of 3.76 cubic meters of water in kilograms, we need to convert cubic meters to cubic centimeters and then multiply it by the mass per cubic centimeter.
1 cubic meter = 1000000 cubic centimeters (since 1 meter = 100 centimeters)
So, 3.76 cubic meters = 3.76 * 1000000 cubic centimeters
Now, since each cubic centimeter of water has a mass of exactly 1 gram, we can say that the mass of 3.76 cubic meters of water is equal to the volume in cubic centimeters.
Therefore, the mass of 3.76 cubic meters of water is 3.76 * 1000000 grams.
To convert grams to kilograms, we divide the value by 1000.
So, the mass of 3.76 cubic meters of water is (3.76 * 1000000) / 1000 kilograms.
Simplifying, we get 3760 kilograms.
Therefore, the mass of 3.76 cubic meters of water is 3760 kilograms.
(b) The mass flow rate of water from the container is given by the mass of water divided by the time it takes to drain the container.
To find the mass flow rate, we need to determine the mass of 59.1 cubic meters of water first using the method described in part (a).
The mass of 59.1 cubic meters of water is 59.1 * 1000000 grams.
To convert grams to kilograms, we divide the value by 1000.
So, the mass of 59.1 cubic meters of water is (59.1 * 1000000) / 1000 kilograms.
Simplifying, we get 59100 kilograms.
Therefore, the mass of 59.1 cubic meters of water is 59100 kilograms.
Now, we can calculate the mass flow rate by dividing the mass (59100 kilograms) by the time (10.4 hours) it takes to drain the container.
To convert hours to seconds, multiply the value by 3600 since there are 3600 seconds in one hour.
So, the time in seconds is 10.4 hours * 3600 seconds/hour.
Now, divide the mass (59100 kilograms) by the time in seconds (10.4 hours * 3600 seconds/hour).
The mass flow rate of water from the container is 59100 kilograms / (10.4 hours * 3600 seconds/hour).
Simplifying, we get the mass flow rate to be approximately 1.548 kg/s.
Therefore, the mass flow rate of water from the container is approximately 1.548 kg/s.
a. 3.76m^3*10^-6cm^3/m^3 = 3.76*10^-6cm^3.
1g = (1/1000)kg = 10^-3kg.
Mass = 10^-3kg/cm^3 * 3.76^10^-6cm^3 = 3.76*10^-9kg.
b. Rate = 59.1m^3 / 10.4h = 5.68m^3/h.
5.68m^3 * 10^-9kg/m^3 = 5.68*10^-9kg.
Rate = 5.68*10^-9kg/h * (1/3600)h/s = 1.58*10^-12kg/s.