A rectangular block has a length 10cm, breadth 5cm and height 2.0cm. If it lies on a horizontal surface, and has density 1000kg/m^3, calculate the pressure it exerts on the surface.
A cylindrical jar of radius 7.0cm and height 25cm, is filled with liquid 0.80g/cm^3. What pressure exerted at the bottom of the jar by the liquid?
what is the area of the face lying on the surface?
pressure = weight / area
mass = volume * density
weight = mass * g
pressure = force/area
1225π cm^3 * 0.80g/cm^3 * 1kg/1000g * 9.81 N/kg / 49πcm^2 = 0.1962 N/cm^2
Well, well, well! Let's crunch some numbers and bring out the laughs!
For the rectangular block, we need to calculate the pressure it exerts on the surface. So, let's start by converting the dimensions to meters. The length is 10 cm, which is 0.1 m. The breadth is 5 cm, which is 0.05 m. And the height is 2.0 cm, which is 0.02 m.
Now, to find the pressure, we need to know the weight of the block. The weight is equal to the density times the volume times the acceleration due to gravity. In this case, the density is 1000 kg/m^3, the volume is length times breadth times height (0.1 m * 0.05 m * 0.02 m), and the acceleration due to gravity is 9.8 m/s^2.
So, the weight of the block is equal to 1000 kg/m^3 * 0.1 m * 0.05 m * 0.02 m * 9.8 m/s^2.
Now, if we divide the weight by the surface area of the block, which is length times breadth (0.1 m * 0.05 m), we can find the pressure!
But wait! Before we calculate the pressure, let me tell you a joke! Why don't scientists trust atoms? Because they make up everything!
Okay, back to business. Let's calculate the pressure now!
To calculate the pressure exerted by each block, we need to use the formula:
Pressure = Force/Area
For the rectangular block:
1. Calculate the volume of the block:
Volume = length × breadth × height
= 10 cm × 5 cm × 2.0 cm
= 100 cm³
2. Convert the volume to SI unit (m³):
Volume = 100 cm³ = 100 × (1/100) m³
= 1 m³
3. Calculate the mass of the block:
Mass = density × volume
= 1000 kg/m³ × 1 m³
= 1000 kg
4. Calculate the weight of the block:
Weight = mass × gravity
= 1000 kg × 9.8 m/s²
= 9800 N
5. Calculate the area of the surface it is exerting pressure on:
Area = length × breadth
= 10 cm × 5 cm
= 50 cm²
6. Convert the area to SI unit (m²):
Area = 50 cm² = 50 × (1/100) m²
= 0.5 m²
7. Calculate the pressure exerted by the block:
Pressure = Weight/Area
= 9800 N / 0.5 m²
= 19600 Pa
Therefore, the pressure exerted by the rectangular block is 19600 Pa.
Now let's calculate the pressure exerted by the liquid in the cylindrical jar:
1. Calculate the volume of the liquid:
Volume = π × radius² × height
= π × (7.0 cm)² × 25 cm
= 3848.46 cm³
2. Convert the volume to SI unit (m³):
Volume = 3848.46 cm³ = 3848.46 × (1/1000000) m³
= 0.00384846 m³
3. Calculate the mass of the liquid:
Mass = density × volume
= 0.80 g/cm³ × 0.00384846 m³
= 3.078768 g
4. Convert the mass to SI unit (kg):
Mass = 3.078768 g = 3.078768 × (1/1000) kg
= 0.003078768 kg
5. Calculate the weight of the liquid:
Weight = mass × gravity
= 0.003078768 kg × 9.8 m/s²
= 0.0301560624 N
6. Calculate the area of the bottom of the jar:
Area = π × radius²
= π × (7.0 cm)²
= 153.93804 cm²
7. Convert the area to SI unit (m²):
Area = 153.93804 cm² = 153.93804 × (1/10000) m²
= 0.015393804 m²
8. Calculate the pressure exerted by the liquid:
Pressure = Weight/Area
= 0.0301560624 N / 0.015393804 m²
= 1.959 Pa
Therefore, the pressure exerted at the bottom of the jar by the liquid is approximately 1.959 Pa.
To calculate the pressure exerted by the rectangular block on the surface, we need to know the weight of the block. The weight can be calculated using the formula:
Weight = Volume × Density × Gravity
Where Volume is the product of length, breadth, and height, Density is the density of the block, and Gravity is the acceleration due to gravity (approximately 9.8 m/s^2).
Let's calculate the weight of the rectangular block first:
Volume = Length × Breadth × Height
= 10 cm × 5 cm × 2.0 cm
= 100 cm^3
Density = 1000 kg/m^3
So, the density in terms of grams/cm^3 would be 1000 g/m^3, which is equal to 0.001 g/cm^3.
Weight = Volume × Density × Gravity
= 100 cm^3 × 0.001 g/cm^3 × 9.8 m/s^2
= 0.98 g
Now, to calculate the pressure exerted by the block, we'll use the formula:
Pressure = Weight/Area
The area in this case is the product of length and breadth, which is 10 cm × 5 cm = 50 cm^2.
Pressure = Weight/Area
= 0.98 g / 50 cm^2
= 0.0196 g/cm^2
Therefore, the pressure exerted by the rectangular block on the surface is 0.0196 g/cm^2.
To calculate the pressure exerted by the liquid in the cylindrical jar at the bottom, we'll use a similar approach. First, we need to calculate the weight of the liquid:
Volume = π × Radius^2 × Height
= π × (7.0 cm)^2 × 25 cm
= 3848.451 cm^3
Density = 0.80 g/cm^3
Weight = Volume × Density × Gravity
= 3848.451 cm^3 × 0.80 g/cm^3 × 9.8 m/s^2
= 30029.98 g
Now, to calculate the pressure exerted by the liquid, we need to determine the area of the bottom of the jar, which is the same as the area of the circular shape:
Area = π × Radius^2
= π × (7.0 cm)^2
= 153.938 cm^2
Pressure = Weight/Area
= 30029.98 g / 153.938 cm^2
= 195.047 g/cm^2
Therefore, the pressure exerted at the bottom of the jar by the liquid is 195.047 g/cm^2.