A marble cylinder that has a diameter of 42cm and stands 1.25m tall rests on a flat tile deck. What is the pressure excerted on the deck by the cylinder?
I do not know density of marble, rho.
Weight = rho g * volume
volume = pi r^2 h
so
Weight = rho g (pi r^2 h)
pressure = weight/area where area = pi r^2
so
pressure = rho g h
Density of marble is 2.7 x 10^3 kg/m^3... Idk if that helps?
To calculate the pressure exerted by the marble cylinder on the deck, we need to know the weight of the cylinder and the area over which it is exerting the force.
1. Calculate the weight of the marble cylinder:
The weight of an object can be calculated using the formula: weight = mass x acceleration due to gravity.
The mass of the cylinder can be calculated using the formula: mass = density x volume.
The density of marble is approximately 2,700 kg/m³.
The volume of the cylinder can be calculated using the formula: volume = π x radius^2 x height.
The radius of the cylinder is half of the diameter, so radius = 42 cm / 2 = 21 cm = 0.21 m.
The height of the cylinder is given as 1.25 m.
Calculating the volume of the cylinder: volume = π x (0.21 m)^2 x 1.25 m = 0.2308 m³.
Calculating the mass of the cylinder: mass = 2,700 kg/m³ x 0.2308 m³ = 623.16 kg.
Calculating the weight of the cylinder: weight = 623.16 kg x 9.8 m/s² ≈ 6,105 N.
2. Calculate the area over which the force is exerted:
The area of the bottom of the cylinder is equal to the area of a circle with radius 0.21 m.
Calculating the area of the circle: area = π x (0.21 m)^2 ≈ 0.138 m².
3. Calculate the pressure:
Pressure is defined as force (weight) divided by the area over which it is exerted.
Calculating the pressure: pressure = weight / area = 6,105 N / 0.138 m² ≈ 44,284 Pa.
Therefore, the pressure exerted on the deck by the marble cylinder is approximately 44,284 Pascals (Pa).
To find the pressure exerted on the deck by the cylinder, we need to use the formula:
Pressure = Force / Area
Step 1: Calculate the force exerted by the cylinder on the deck.
Force = Weight = Mass * Gravity
Step 2: Calculate the mass of the cylinder.
The volume of a cylinder can be calculated using the formula:
Volume = π * r^2 * h
where r is the radius and h is the height of the cylinder.
Given that the diameter of the cylinder is 42 cm, the radius (r) can be obtained by dividing the diameter by 2:
r = d / 2 = 42 cm / 2 = 21 cm = 0.21 m
The height (h) of the cylinder is given as 1.25 m.
Using these values, we can now calculate the volume:
Volume = π * (0.21 m)^2 * 1.25 m
Step 3: Calculate the mass of the cylinder.
The density of marble is typically around 2.5 g/cm^3.
Mass = Density * Volume
However, we need to convert the density from g/cm^3 to kg/m^3 because the volume is in cubic meters.
Density = 2.5 g/cm^3 = 2500 kg/m^3
Now we can calculate the mass:
Mass = 2500 kg/m^3 * Volume
Step 4: Calculate the force.
Force = Mass * Gravity
The acceleration due to gravity is approximately 9.8 m/s^2.
Force = Mass * 9.8 m/s^2
Step 5: Calculate the pressure exerted on the deck.
Now that we have the force, we need to find the area of contact between the cylinder and the deck to calculate the pressure.
The contact area is the base of the cylinder, which is a circle with radius r.
Area = π * r^2
Since we already calculated the value of r as 0.21 m, we can substitute it into the formula:
Area = π * (0.21 m)^2
Now we can calculate the pressure:
Pressure = Force / Area
By substituting the values of Force and Area into this formula, we can find the pressure exerted on the deck by the cylinder.