Three cylindrical blocks x, y and z are made of different materials of densities 2g/cm3, 5g/cm3 and 10g/cm3 respectively. If the side of each block resting on a level surface has an area of 2cm2, 4cm2 and 6cm2 and the height of block x is 10cm calculate;
1) weight of block x
2) pressure exerted by block x on the surface
3) height of blocks y and z if the pressure exerted by each block on the surface is the same
1) weight= mass x gravity
mass= density x volume
volume= area x height
volume= 10 x 2= 20
mass= 20 x 2= 40g
40g=0.04kg
weight= 0.04 x 10= 0.4N
2) P= 0.4/2 x 0.01
P= 2000Pa
3) I need help with this last part myself. If someone would be so kind as to help.
To answer these questions, we'll need to use the formulas for weight, pressure, and density. Let's go step by step.
1) Weight of block x:
Weight is calculated using the formula:
Weight = Density * Volume * Acceleration due to gravity.
Given:
Density of block x = 2g/cm³
Height of block x = 10cm
Area of the side resting on the surface = 2cm²
To calculate the volume of block x, multiply the area of the base by the height:
Volume of block x = Area * Height
Volume of block x = 2cm² * 10cm
Volume of block x = 20cm³
Now we can calculate the weight of block x:
Weight of block x = Density of block x * Volume of block x * Acceleration due to gravity
Weight of block x = 2g/cm³ * 20cm³ * 9.8m/s² (conversion of g to m/s²)
Weight of block x = 392g
Therefore, the weight of block x is 392g.
2) Pressure exerted by block x on the surface:
Pressure is calculated using the formula:
Pressure = Force / Area
Given:
Weight of block x = 392g (or 0.392kg)
Area of the side resting on the surface = 2cm²
Now, we need to convert the weight to force using the equation:
Weight = Force * Acceleration due to gravity
Rearranging the formula, we can find the force:
Force = Weight / Acceleration due to gravity
Force = 0.392kg * 9.8m/s²
Force = 3.8416N
Now we can calculate the pressure exerted by block x:
Pressure = Force / Area
Pressure = 3.8416N / 2cm²
Pressure = 1.9208N/cm²
Therefore, the pressure exerted by block x on the surface is 1.9208N/cm².
3) Height of blocks y and z if the pressure exerted by each block on the surface is the same:
Since the pressure exerted by each block is the same, we can equate the pressures:
Pressure of block x = Pressure of block y = Pressure of block z
Using the formula for pressure, we can write:
Force of block x / Area of block x = Force of block y / Area of block y = Force of block z / Area of block z
Since the areas are given in the question, we can equate the forces:
Force of block x = Force of block y = Force of block z
Now we know that the weight of each block is the same. Using the weight formula (Weight = Density * Volume * Acceleration due to gravity), we can write:
Density of block x * Volume of block x = Density of block y * Volume of block y = Density of block z * Volume of block z
Dividing these equations, we can eliminate the densities:
Volume of block x / Volume of block y = Volume of block y / Volume of block z
Since the areas are given and the volumes are calculated by multiplying the area by the height, we can write:
(Height of block x * Area of block x) / (Height of block y * Area of block y) = (Height of block y * Area of block y) / (Height of block z * Area of block z)
Now we can substitute the given values:
(10cm * 2cm²) / (Height of block y * 4cm²) = (Height of block y * 4cm²) / (Height of block z * 6cm²)
Simplifying the equation:
20cm² / (Height of block y * 4cm²) = (Height of block y * 4cm²) / (Height of block z * 6cm²)
Cross-multiplying:
20cm² * (Height of block y * 4cm²) = (Height of block y * 4cm²) * (Height of block z * 6cm²)
Simplifying further:
80cm^4 = Height of block y * Height of block z * 24cm^4
Dividing both sides by 24cm^4:
3.33 = Height of block y * Height of block z
Since both heights are positive, the product of their heights cannot be negative. Therefore, it is not possible to determine specific heights for blocks y and z given the equal pressure exerted.
In conclusion, the height of blocks y and z cannot be determined with the information provided since there are multiple possible combinations that satisfy the given conditions.