A rectangular metal block with side 1.5𝑚 by 1.2𝑚 by 1.0𝑚 rests on a horizontal surface .If the density of
the metal is 7000𝑘𝑔/𝑚3, calculates; i. Volume of the metal block, ii. Mass of metal block, iii. The
difference between maximum and the minimum pressure that the block can exerts on the surface
volume = 1.5m*1.2m*1.0m = 1.8 m^3
mass = volume * density
since pressure = force/area,
maximum pressure is when the smallest face is resting on the surface
minimum pressure is when the largest face is resting on the surface.
I assume you know how to find the area of a rectangular face.
remember weight = mass * g
and as you know pressure = weight in Newtons / area in square meters
in Pascals :)
To find the answers to your questions, we can use basic equations related to density, volume, and pressure.
i. Volume of the metal block:
The volume of a rectangular block can be calculated by multiplying the length, width, and height of the block. In this case, the given dimensions are 1.5 m by 1.2 m by 1.0 m. So, the volume can be calculated as follows:
Volume = Length × Width × Height
Volume = 1.5 m × 1.2 m × 1.0 m
Volume = 1.8 m³
ii. Mass of the metal block:
To find the mass of an object, we can use the equation:
Mass = Density × Volume
Given density is 7000 kg/m³, and the volume we found in the previous step is 1.8 m³. So, substituting these values into the equation, we can calculate the mass:
Mass = 7000 kg/m³ × 1.8 m³
Mass = 12600 kg
iii. Difference between maximum and minimum pressure exerted on the surface:
When an object rests on a surface, it exerts pressure on that surface. In this case, the block is in equilibrium, so the pressure exerted on the surface will be uniform. The pressure exerted by an object can be calculated using the equation:
Pressure = Force / Area
Since the block is at rest, the weight of the block is the force acting downward. The weight of the block can be calculated using the equation:
Weight = Mass × Gravity
The gravitational acceleration is approximately 9.8 m/s². Assuming the block rests on a flat surface, the total area in contact with the surface is equal to the product of the length and width of the block.
Therefore, the minimum pressure exerted on the surface is:
Minimum Pressure = Weight / Total Area
And the maximum pressure exerted on the surface is the same as the minimum pressure since the block is in equilibrium.
Hope this helps!