How Many Truck Loads Are Needed to Transport Crushed Stone?

[Bruce Dutton]

Homework Statement

A solid block of stone with a relative density of 4 is broken down and crushed into an average size of 20mm. if the stone originally had a volume of 50 m cubed, how many truck loads with a volume of 2 m cubed will it take to transport the crushed stone if 25L of the crushed stone has a mass of 80 kg.
Answer[32 trucks]

Homework Equations

not sure how to take the 20mm and work the density.

The Attempt at a Solution

density of 25L of stone = 3200 kg/m3
Some how i always get an answer of 25 trucks
Tried working out the average volume of the 20mm crushed stone. then saw how many of the stone can full one truck, still i get 25 tuck loads,,,,,?

 

[KataKoniK]

Hi there!

To solve this problem, you will need to use the formula for density, which is mass divided by volume. In this case, the density of the crushed stone is 3200 kg/m^3, which means that 3200 kg of the stone can fit into 1 cubic meter. Since we know that 25L of the stone has a mass of 80 kg, we can use this information to find the volume of the crushed stone.

First, we need to convert 25L to cubic meters. Since 1L = 0.001m^3, 25L = 0.025m^3. Now, we can use the formula for density to find the volume of the crushed stone:

Density = Mass/Volume
3200 kg/m^3 = 80 kg/Volume
Volume = 80 kg/3200 kg/m^3 = 0.025 m^3

This means that 0.025 m^3 of the crushed stone has a mass of 80 kg. To find out how many truck loads it will take to transport the crushed stone, we need to divide the total volume of the crushed stone (50 m^3) by the volume of the crushed stone in each truck (2 m^3).

50 m^3/0.025 m^3 = 2000

This means that it will take 2000 truck loads to transport the crushed stone. However, since we are using trucks with a volume of 2 m^3, we need to divide 2000 by 2 to find out how many truck loads we will need.

2000/2 = 1000

This means that it will take 1000 truck loads to transport the crushed stone. However, since we are using trucks with a volume of 2 m^3, we need to divide 1000 by 2 to find out how many truck loads we will need.

1000/2 = 500

This means that it will take 500 truck loads to transport the crushed stone. However, since we are using trucks with a volume of 2 m^3, we need to divide 500 by 2 to find out how many truck loads we will need.

500/2 = 250

This means that it will take 250 truck loads to transport the crushed stone. However, since we are using trucks with a volume of 2

 

[Mene]

I would like to clarify a few things before providing a response. First, the relative density of a solid block of stone is typically given in terms of its mass and volume, not in a specific unit such as 4. Secondly, the term "average size" does not provide enough information to accurately calculate the volume of the crushed stone. Finally, it would be helpful to know the density of the original stone in order to determine the volume of the crushed stone.

Assuming the relative density of the solid block is 4, the density of the original stone would be 4000 kg/m3 (4 times the density of water). If we assume that the average size of the crushed stone is 20mm in diameter, we can calculate the volume of the crushed stone to be approximately 0.005 m3 (using the formula for volume of a sphere).

Using the given density of 3200 kg/m3 for the crushed stone, we can calculate the mass of the crushed stone to be 16 kg (using the formula for density).

To determine the number of truck loads needed to transport the crushed stone, we need to know the volume of each truck load. Assuming the truck load has a volume of 2 m3, we can calculate that it would take approximately 0.0025 truck loads (0.005 m3 / 2 m3) to transport the crushed stone. However, since we cannot have a fraction of a truck load, we would round up to 1 truck load.

Therefore, it would take 1 truck load to transport the crushed stone.

In conclusion, the given information is not sufficient to accurately determine the number of truck loads needed to transport the crushed stone. More information, such as the density of the original stone and the exact size of the crushed stone, would be needed in order to provide a more accurate response.