To determine the maximum and minimum pressure exerted by the copper block on a horizontal surface, we can follow these steps:
-
Calculate the volume of the copper block: \[ \text{Volume} = \text{length} \times \text{width} \times \text{height} = 5 , \text{cm} \times 3 , \text{cm} \times 2 , \text{cm} = 30 , \text{cm}^3 \]
-
Calculate the mass of the copper block using its density: \[ \text{Density of copper} = 8.9 , \text{g/cm}^3 \] \[ \text{Mass} = \text{Density} \times \text{Volume} = 8.9 , \text{g/cm}^3 \times 30 , \text{cm}^3 = 267 , \text{g} \] Converting grams to kilograms: \[ \text{Mass} = 0.267 , \text{kg} \]
-
Calculate the weight (force due to gravity) of the copper block: \[ \text{Weight} = \text{Mass} \times \text{g} = 0.267 , \text{kg} \times 10 , \text{N/kg} = 2.67 , \text{N} \]
-
Calculate the contact area for the maximum and minimum pressure:
- Maximum Pressure: The maximum pressure occurs when the block is resting on its smallest face (2 cm x 3 cm). \[ \text{Area}_{\text{max}} = 2 , \text{cm} \times 3 , \text{cm} = 6 , \text{cm}^2 = 6 \times 10^{-4} , \text{m}^2 \]
- Minimum Pressure: The minimum pressure occurs when the block is resting on its largest face (5 cm x 3 cm). \[ \text{Area}_{\text{min}} = 5 , \text{cm} \times 3 , \text{cm} = 15 , \text{cm}^2 = 15 \times 10^{-4} , \text{m}^2 \]
-
Calculate the maximum and minimum pressure:
-
Maximum Pressure: \[ \text{Pressure}{\text{max}} = \frac{\text{Weight}}{\text{Area}{\text{max}}} = \frac{2.67 , \text{N}}{6 \times 10^{-4} , \text{m}^2} \approx 4450 , \text{N/m}^2 = 4450 , \text{Pa} \]
-
Minimum Pressure: \[ \text{Pressure}{\text{min}} = \frac{\text{Weight}}{\text{Area}{\text{min}}} = \frac{2.67 , \text{N}}{15 \times 10^{-4} , \text{m}^2} \approx 1780 , \text{N/m}^2 = 1780 , \text{Pa} \]
-
Summary of Results:
- Maximum Pressure: \( 4450 , \text{Pa} \)
- Minimum Pressure: \( 1780 , \text{Pa} \)