an aluminum cylinder, of height h=2ocm and of radius r=1ocm, rests with its base on a horizontal table. Density of aluminum P=2700kg/m^3

a-calculate the weight of the cylinder take g=10N/kg
b-what is the value of the force exerted by the table on the cylinder?
c-deduce the magnitude of the force exerted by the cylinder on the table
d-calculate the pressure exerted by the cylinder on the table

Defining z axis up:

area of base of cylinder A= pi r^2
where r = 20 cm = .20 meter

height of cylinder = .10 meter

volume of cylinder V= pi r^2 h
= pi (.2)^2 (.1)

weight of cylinder W = g V = 10 V in Newtons

b) +W

c) -W

d) W/A in Newtons/meter^2 or Pascals

a) To calculate the weight of the cylinder, we need to determine the volume of the cylinder first. The volume of a cylinder is given by the formula V = π * r^2 * h. Substituting the given values of r (10 cm) and h (20 cm) into the formula:

V = π * (10 cm)^2 * (20 cm) = π * 100 cm^2 * 20 cm = 2000 π cm^3.

Next, we convert the volume from cubic centimeters to cubic meters because the density is given in kg/m^3. Since 1 m = 100 cm, we divide the volume by 1,000,000 (10^6) to obtain the volume in cubic meters:

V = (2000 π cm^3) / (10^6 cm^3/m^3) = 0.002 π m^3.

Now, we can calculate the mass of the cylinder using the density formula: density = mass / volume. Rearranging the formula to solve for mass:

mass = density * volume = (2700 kg/m^3) * (0.002 π m^3).

Finally, we can calculate the weight using the formula: weight = mass * gravitational acceleration (g) = mass * 10 N/kg. Plugging in the value of mass:

weight = (2700 kg/m^3) * (0.002 π m^3) * (10 N/kg) ≈ 169.65 N.

Therefore, the weight of the cylinder is approximately 169.65 N.

b) The value of the force exerted by the table on the cylinder is equal in magnitude but opposite in direction to the weight of the cylinder. So, the force exerted by the table on the cylinder is 169.65 N, directed upward.

c) The magnitude of the force exerted by the cylinder on the table is equal in magnitude but opposite in direction to the force exerted by the table on the cylinder. Therefore, the magnitude of the force exerted by the cylinder on the table is also 169.65 N.

d) To calculate the pressure exerted by the cylinder on the table, we need to divide the force exerted by the cylinder on the table by the area of contact between the cylinder and the table. The area of the base of the cylinder is given by the formula:

A = π * r^2 = π * (10 cm)^2.

Converting the radius from centimeters to meters:

A = π * (0.1 m)^2 = π * 0.01 m^2 = 0.01 π m^2.

Now we can calculate the pressure using the formula: pressure = force / area. Plugging in the value of the force exerted by the cylinder on the table:

pressure = (169.65 N) / (0.01 π m^2) ≈ 5396.76 N/m^2.

Therefore, the pressure exerted by the cylinder on the table is approximately 5396.76 N/m^2, or 5396.76 Pa.