3.201 kg of gold in rock
Therefore rock is 89.67% gold
A prospector finds a solid rock composed of granite ( = 2650 kg/m3) and gold. The volume of the rock is 3.05 10-4 m3 and its mass is 3.57 kg.
What mass of gold is contained in the rock?
I thought that I could used some ratio, but I have no idea how. Our teacher hasn't even talked about this. Any help?
You know the density of granite.
mass granite= volumerock*density
mass gold= 3.57- massgranite.
I just had a note from another teacher that there is an error here. The mass of granite= volumegranite*densitygranite, and the volume of granite is not the same as the volume of rock. This makes technically the problem impossible to solve.
2 answers
Part 1:
a) With the dimensions of the pyramid and blocks given above, how many blocks were required to build the pyramid?
b) The blocks are made of sandstone with a density of about 2.00 g/cm3. What is the mass of the average block?
c) The Egyptian's sled system had a rather high coefficient of static friction (µ= 0.7) but a much lower coefficient of kinetic friction (µ= 0.3**). How much force is required to start a block moving?
d) Estimate the amount of force that one person can sustain for ten hours of work. (Think about the weight of a hiker's backpack.) Using this value, how many people does it take to pull a block at constant velocity.
e) Estimate a comfortable walking speed for an average person. Assume that the workers could only walk at half this speed while they were pulling a block, but that they could walk at this speed on the trip from the pyramid back to the quarry. At these speeds, how many blocks can one crew, of the size calculated above, move the 5 km from quarry to pyramid in one ten hour work day? Truncate this number to an integer.
f) If each worker can generate 5 times their usual force for a short time, by bracing their feet against ridges or pegs that are fixed in place, and pulling with all of their might, how long does it take to accelerate a block to the walking speed? Are the forces experienced by the worker reasonable?
Part 2:
a) Now consider the process of lifting the blocks to the required heights. If a work crew double the size of the crew used to move the block across flat land was used to move the block up a ramp, what is the steepest angle the ramp could have? At this angle, how long would the ramp to the top of the pyramid have to be? How long would it take the crew to move the block to this height?
b) Use the results of your calculations and the information provided about the pyramid to devise a model for the time required for one crew to raise all of the blocks to the required heights. Use a simple model, but make certain that the estimate is as accurate as the estimate for the time to transport the blocks from the quarry.
c) Use your answers to 1a, 1e, and 2b to calculate a total number of worker hours required to build the pyramid.
d) Considering that the pyramid was built in 20 years, and the workers only worked on it for three months out of each year, use the previous assumption of a ten hour work day to calculate the total number of people required. For a better estimate, guess at the number of people that were needed in addition to those that have been considered in this problem.
a) With the dimensions of the pyramid and blocks given above, how many blocks were required to build the pyramid?
b) The blocks are made of sandstone with a density of about 2.00 g/cm3. What is the mass of the average block?
c) The Egyptian's sled system had a rather high coefficient of static friction (µ= 0.7) but a much lower coefficient of kinetic friction (µ= 0.3**). How much force is required to start a block moving?
d) Estimate the amount of force that one person can sustain for ten hours of work. (Think about the weight of a hiker's backpack.) Using this value, how many people does it take to pull a block at constant velocity.
e) Estimate a comfortable walking speed for an average person. Assume that the workers could only walk at half this speed while they were pulling a block, but that they could walk at this speed on the trip from the pyramid back to the quarry. At these speeds, how many blocks can one crew, of the size calculated above, move the 5 km from quarry to pyramid in one ten hour work day? Truncate this number to an integer.
f) If each worker can generate 5 times their usual force for a short time, by bracing their feet against ridges or pegs that are fixed in place, and pulling with all of their might, how long does it take to accelerate a block to the walking speed? Are the forces experienced by the worker reasonable?
Part 2:
a) Now consider the process of lifting the blocks to the required heights. If a work crew double the size of the crew used to move the block across flat land was used to move the block up a ramp, what is the steepest angle the ramp could have? At this angle, how long would the ramp to the top of the pyramid have to be? How long would it take the crew to move the block to this height?
b) Use the results of your calculations and the information provided about the pyramid to devise a model for the time required for one crew to raise all of the blocks to the required heights. Use a simple model, but make certain that the estimate is as accurate as the estimate for the time to transport the blocks from the quarry.
c) Use your answers to 1a, 1e, and 2b to calculate a total number of worker hours required to build the pyramid.
d) Considering that the pyramid was built in 20 years, and the workers only worked on it for three months out of each year, use the previous assumption of a ten hour work day to calculate the total number of people required. For a better estimate, guess at the number of people that were needed in addition to those that have been considered in this problem.
1 answer