A rectangular metal block with side 1.5m, by 1.2 by 1.0 rests a horizontal surface. If the density of metal is 7000kg/m³ calculate
Difference btn maximum and minimum pressure that the block can exert
To calculate the difference between the maximum and minimum pressure that the block can exert, we need to consider the weight of the block and the area over which it is distributed.
First, let's calculate the weight of the block:
The volume of the block is given by its dimensions:
Volume = length × width × height
Volume = 1.5m × 1.2m × 1.0m
Volume = 1.8m³
Next, we can calculate the weight of the block using the density of the metal:
Weight = density × volume
Weight = 7000kg/m³ × 1.8m³
Weight = 12600kg
The weight of the block is 12600kg.
To calculate the maximum pressure, we need to consider the area over which the weight is distributed. Since the block is resting on a horizontal surface, the weight will be distributed evenly over the entire base area.
The base area is given by the length and width of the block:
Base area = length × width
Base area = 1.5m × 1.2m
Base area = 1.8m²
Now we can calculate the maximum pressure:
Maximum pressure = Weight / Base area
Maximum pressure = 12600kg / 1.8m²
Maximum pressure ≈ 7000Pa
To calculate the minimum pressure, we can consider a specific point on the base of the block. As the weight is distributed evenly over the base, the minimum pressure will be exerted at the edge of the base.
Since the block is rectangular, the edge length will be the same as the width or the length. Let's consider the length for this calculation:
Width = 1.2m
Minimum pressure = Weight / Area of a point
Minimum pressure = 12600kg / (1.5m × 1.0m)
Minimum pressure ≈ 8400Pa
Therefore, the difference between the maximum and minimum pressure that the block can exert is:
Difference = Maximum pressure - Minimum pressure
Difference = 7000Pa - 8400Pa
Difference = -1400Pa
Note: The negative difference indicates that the minimum pressure is greater than the maximum pressure. However, in this context, it is not physically meaningful because the minimum pressure occurs at a specific point on the base while the maximum pressure is distributed over the entire base.
mass of the block = volume * density
force (weight) = m * g
pressure = force / area ... newton per m^2 is a Pascal
max pressure when resting on smallest side ... 1.2 m x 1.0 m
min pressure when resting on largest side ... 1.2 m x 1.5 m