Question
A block of copper of density 8.9g\cm measures 5cm by 3cm by 2cm .Given that the force of gravity is 10n\kg .Determine;A.the maximum pressure.B;the minimum pressure that it can exert on a horrizontal surface
Answers
GPT-4o mini
To determine the maximum and minimum pressure exerted by the copper block on a horizontal surface, we can follow these steps:
1. **Calculate the volume of the copper block:**
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height} = 5 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm} = 30 \, \text{cm}^3
\]
2. **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:
\[
\text{Mass} = 0.267 \, \text{kg}
\]
3. **Calculate the weight (force due to gravity) of the copper block:**
\[
\text{Weight} = \text{Mass} \times \text{g} = 0.267 \, \text{kg} \times 10 \, \text{N/kg} = 2.67 \, \text{N}
\]
4. **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).
\[
\text{Area}_{\text{min}} = 5 \, \text{cm} \times 3 \, \text{cm} = 15 \, \text{cm}^2 = 15 \times 10^{-4} \, \text{m}^2
\]
5. **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:** \( 1780 \, \text{Pa} \)
1. **Calculate the volume of the copper block:**
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height} = 5 \, \text{cm} \times 3 \, \text{cm} \times 2 \, \text{cm} = 30 \, \text{cm}^3
\]
2. **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:
\[
\text{Mass} = 0.267 \, \text{kg}
\]
3. **Calculate the weight (force due to gravity) of the copper block:**
\[
\text{Weight} = \text{Mass} \times \text{g} = 0.267 \, \text{kg} \times 10 \, \text{N/kg} = 2.67 \, \text{N}
\]
4. **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).
\[
\text{Area}_{\text{min}} = 5 \, \text{cm} \times 3 \, \text{cm} = 15 \, \text{cm}^2 = 15 \times 10^{-4} \, \text{m}^2
\]
5. **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:** \( 1780 \, \text{Pa} \)