1. If the sun which is 93,000,000 miles away away from Earth was to go out, how long would it take for us to know that this had happened? Light travels at a speed of 3 x 10^8 meters/second.
2. What would the density be (in g/cm^3) of a block that is 4 cm by 15 cm by 12 cm, and has a mass of 4.3 kg?
3. An object has a density of 8.96 g/cm^3. It has a mass of 405 grams. What is its volume?
4. An object has a density of 3.75 g/cm^3. It has a volume of 9.3 liters. What is its mass?© BrainMass Inc. brainmass.com December 24, 2021, 4:54 pm ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
1. To solve this problem we must convert the distance from miles to meters or kilometers.
We know 5 miles = 8 Km ===> 1 mile = 8/5 Km = 1.6Km
Thus the distance from earth to sun is,
D = 93,000,000 * 1.6 Km = 93,000,000 * 1.6 * 1000 meters
= 93 * 10^6 * 1.6 * 10^3 = 148.8 * 10^9 meters
Suppose, the last light pule from the sun leaves it at t=0 and that pulse will be our last detected light from the sun. The pulse travels with a speed of 3 * 10^8 m/s and has to cover a distance D. It will take a time to reach the earth. This time is the required answer to our question.
We have Velocity = Distance/Time
From this, Time = Distance/Velocity
Thus our answer is T = D/3*10^8
= 148.8 * 10^9 meters/3*10^8 = (148.8/3) * 10 = 496 Sec
Or, T = 496/60 = 8.26 Minutes
2. Density is defined to be the ratio of mass to volume. Here also remember to put the numbers in the same units.
Density = Mass/Volume
First, the volume of the block = 4 * 15 * 12 = 720 cm^3
Mass of the block = 4.3Kg = 4.3*10^3 Grams
Now density of the block = 4.3*10^3g/720cm^3 = 5.972 g/cm^3
3. Here also we will use the definition of density
From above answer, Volume = Mass/Density
= 405grams/(8.96g/cm^3) = 45.2 cm^3 ---Answer
4. Again, from answer to qn 3, Mass = Density * Volume
Remember to convert 9.3 Liters to cm^3
We have, 1 liter = 1000 cm^3
Thus, 9.3 liters = 9.3*10^3 cm^3
Now, Mass = (3.75g/cm^3) * 9.3*10^3 cm^3
= 34875 grams
= 34.875 Kg
If you are worried about recalling the formula mass/vol = density, try dimensional analysis to check the answer. For example, you can see that Mass/volume ==> number in grams/number in cm^3. Which yields the unit as g/cm^3 which is the unit of density. This method is the easiest way to check your answer to any question.© BrainMass Inc. brainmass.com December 24, 2021, 4:54 pm ad1c9bdddf>