Certainly! Let's work through each of these questions step-by-step.
### Question 4:
A force of 16 N acts on an area of [tex]\(50 \, \text{cm}^2\)[/tex]. What is the magnitude of the pressure in pascal?
First, we need to convert the area from [tex]\(\text{cm}^2\)[/tex] to [tex]\(\text{m}^2\)[/tex]:
[tex]\[ 1 \, \text{cm}^2 = 0.0001 \, \text{m}^2 \][/tex]
So:
[tex]\[ 50 \, \text{cm}^2 = 50 \times 0.0001 \, \text{m}^2 = 0.005 \, \text{m}^2 \][/tex]
Now, we use the pressure formula:
[tex]\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \][/tex]
Given:
[tex]\[ \text{Force} = 16 \, \text{N} \][/tex]
[tex]\[ \text{Area} = 0.005 \, \text{m}^2 \][/tex]
So:
[tex]\[ \text{Pressure} = \frac{16 \, \text{N}}{0.005 \, \text{m}^2} = 3200 \, \text{Pa} \][/tex]
### Question 5:
A force of 200 N acts on an area of [tex]\(0.16 \, \text{m}^2\)[/tex]. What is the magnitude of the pressure in pascal?
Using the same pressure formula:
[tex]\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \][/tex]
Given:
[tex]\[ \text{Force} = 200 \, \text{N} \][/tex]
[tex]\[ \text{Area} = 0.16 \, \text{m}^2 \][/tex]
So:
[tex]\[ \text{Pressure} = \frac{200 \, \text{N}}{0.16 \, \text{m}^2} = 1250 \, \text{Pa} \][/tex]
### Question 6:
What is the magnitude of a force which produces a pressure of 7000 Pa while acting on a surface area of [tex]\(0.25 \, \text{m}^2\)[/tex]?
We need to rearrange the pressure formula to solve for Force:
[tex]\[ \text{Force} = \text{Pressure} \times \text{Area} \][/tex]
Given:
[tex]\[ \text{Pressure} = 7000 \, \text{Pa} \][/tex]
[tex]\[ \text{Area} = 0.25 \, \text{m}^2 \][/tex]
So:
[tex]\[ \text{Force} = 7000 \, \text{Pa} \times 0.25 \, \text{m}^2 = 1750 \, \text{N} \][/tex]
### Summary of Answers:
4. The magnitude of the pressure is [tex]\(3200 \, \text{Pa}\)[/tex].
5. The magnitude of the pressure is [tex]\(1250 \, \text{Pa}\)[/tex].
6. The magnitude of the force is [tex]\(1750 \, \text{N}\)[/tex].
