A marble cylinder that has a diameter of 42 cm and stands 1.25 m tall rests on a flat tile deck. What is the pressure exerted on the deck by the cylinder?
You will need to look up the density of marble.
Divide the weight of the marble cylinder (in Newtons) by the base area (in m^2). This will equal
(marble density)*height*g, in N/m^2
To determine the pressure exerted by the marble cylinder on the deck, we need to use the formula for pressure:
Pressure = Force / Area
First, we need to calculate the force exerted by the marble cylinder on the deck. The force is equal to the weight of the cylinder, which can be determined using the formula:
Weight = Mass * Gravity
The mass of the cylinder can be calculated using the formula:
Volume = π * r^2 * h
where r is the radius of the cylinder and h is its height.
Given that the diameter of the cylinder is 42 cm, the radius is half of the diameter:
r = 42 cm / 2 = 21 cm = 0.21 m
The height of the cylinder is given as 1.25 m.
Now we can calculate the volume of the cylinder:
Volume = π * (0.21 m)^2 * 1.25 m
Next, we need to calculate the mass by multiplying the volume by the density of the material that the cylinder is made of. Assuming the density of marble is 2,700 kg/m^3:
Mass = Volume * Density
Using the value obtained from the volume calculation and the density of marble, we can determine the mass of the cylinder.
Finally, we can calculate the weight of the cylinder by multiplying the mass by the acceleration due to gravity, which is approximately 9.8 m/s^2.
Once we have the weight, we can proceed to calculate the pressure exerted on the deck by the cylinder. To do this, we need to determine the area of contact between the cylinder and the deck. Since the cylinder is circular, the area can be calculated using the formula:
Area = π * r^2
Using the radius of the cylinder, we can now calculate the area.
Now, we can substitute the weight and area values into the pressure formula to calculate the pressure exerted by the marble cylinder on the deck.
To calculate the pressure exerted by the cylinder on the deck, we need to use the formula for pressure:
Pressure = Force / Area
In this case, the force is the weight of the cylinder, and the area is the contact area between the cylinder and the deck.
To find the weight of the cylinder, we need to determine its mass and multiply it by the acceleration due to gravity (9.8 m/s^2).
First, let's find the volume of the cylinder:
Volume = π * r^2 * h
where r is the radius (half the diameter) and h is the height of the cylinder.
Given the diameter of the cylinder is 42 cm, the radius (r) would be 42 / 2 = 21 cm = 0.21 m.
The height (h) of the cylinder is given as 1.25 m.
Now we can calculate the volume:
Volume = π * 0.21^2 * 1.25
Next, we need to find the mass of the cylinder. The mass can be determined using the density of marble, which is typically around 2,700 kg/m^3.
Mass = Density * Volume
Finally, we can calculate the weight of the cylinder:
Weight = Mass * acceleration due to gravity
Once we have the weight, we need to consider the contact area between the cylinder and the deck. The contact area would be the area of the circular base of the cylinder.
Area = π * r^2
Now we can calculate the pressure:
Pressure = Weight / Area
Once we have all the values, we can substitute them into the formula to find the pressure exerted by the cylinder on the deck.