A rectangular storage tank 4m long by 3m wide is filled with paraffin to a depth of 2m given that the density of paraffin is 80kg/m^3,caiculate
a)the volume of paraffin
b)the weight of paraffin
c)the mass of paraffin
d)the pressure at the bottom of the tank due to the paraffin
e)if the paraffin is replaced by a denser liquid like water,will be pressure change?explain answer.
190000
a) The volume of the paraffin can be calculated by multiplying the length, width, and depth of the tank. So, V = length × width × depth = 4m × 3m × 2m = 24 cubic meters.
b) To calculate the weight of the paraffin, we need to multiply the volume by the density. The weight or mass is given by the formula: weight = volume × density. So, the weight of the paraffin is 24 cubic meters × 80 kg/m^3 = 1,920 kg.
c) The mass of the paraffin can be directly calculated as the product of the volume and the density, which is 24 cubic meters × 80 kg/m^3 = 1,920 kg.
d) The pressure at the bottom of the tank due to the paraffin can be calculated using the formula: pressure = density × gravitational acceleration × depth. Plugging in the values, we have: pressure = 80 kg/m^3 × 9.8 m/s^2 × 2 m = 1,568 Pascal.
e) If the paraffin is replaced by a denser liquid like water, the pressure will increase. This is because pressure is directly proportional to density, so when a denser liquid replaces a less dense liquid, the pressure at the bottom of the tank will increase.
To find the answers to these questions, we will use various formulas and concepts. Let's go step by step:
a) Volume of paraffin:
The volume of a rectangular prism (or tank) can be calculated using the formula: Volume = Length x Width x Height.
In this case, the length is 4m, the width is 3m, and the depth (height) is 2m.
So, the volume of the paraffin in the tank is: Volume = 4m x 3m x 2m = 24 cubic meters.
b) Weight of paraffin:
Weight is the force exerted by an object due to gravity. It can be calculated using the formula: Weight = Mass x Acceleration due to gravity.
The density of paraffin is given as 80 kg/m^3, and we already know the volume (24 cubic meters). Therefore, we can calculate the mass of the paraffin using the formula: Mass = Density x Volume.
Mass = 80 kg/m^3 x 24 cubic meters = 1920 kg.
c) Mass of paraffin:
The mass of the paraffin is already calculated in the previous step, which is 1920 kg.
d) Pressure at the bottom of the tank due to the paraffin:
Pressure is defined as Force per unit area. The pressure exerted by a fluid is given by the formula: Pressure = Density x Gravitational acceleration x Height.
In this case, the height is the depth of the tank, which is 2m, and the density is 80 kg/m^3. The gravitational acceleration can be taken as approximately 9.8 m/s^2.
Pressure = 80 kg/m^3 x 9.8 m/s^2 x 2m = 1568 Pascals.
e) If the paraffin is replaced by a denser liquid like water, will the pressure change?
Yes, if the liquid is denser (has a higher density) than the paraffin, the pressure will increase. This is because pressure depends on the density of the fluid. As the density increases, the pressure exerted by the fluid also increases. In this case, water is denser than paraffin, so replacing the paraffin with water would increase the pressure at the bottom of the tank.
) An elephant weighs 60 kN and each of its feet has an area of 0.07 m2 in contact with the ground. What is the pressure the elephant exerts on the ground, if:
(a) volume = mass/density
(b) weight = mg
(c) mass = volume * density
(d) using the density of water, pressure = weight/area
(e) from (d), more weight ==> more pressure