Exercise 5: Pressure Calculations 2 – Pressure Worksheet
The key formula for pressure is:
\[
P = \frac{F}{A}
\]
Where:
- \( P \) is the pressure (in N/m² or Pa),
- \( F \) is the force (in N),
- \( A \) is the area (in m²).
We will solve each problem step by step using this formula.
---
Problem 1:
A force of 300 N creates a pressure of 4 N/m². Over what area is the force acting?
#### Solution:
We are given:
- \( F = 300 \, \text{N} \)
- \( P = 4 \, \text{N/m}^2 \)
We need to find the area \( A \). Rearrange the pressure formula to solve for \( A \):
\[
A = \frac{F}{P}
\]
Substitute the given values:
\[
A = \frac{300 \, \text{N}}{4 \, \text{N/m}^2} = 75 \, \text{m}^2
\]
#### Answer:
\[
\boxed{75 \, \text{m}^2}
\]
---
Problem 2:
A pressure of 200 Pa is created over an area of 5 m². What force acts to create this pressure?
#### Solution:
We are given:
- \( P = 200 \, \text{Pa} \)
- \( A = 5 \, \text{m}^2 \)
We need to find the force \( F \). Rearrange the pressure formula to solve for \( F \):
\[
F = P \cdot A
\]
Substitute the given values:
\[
F = 200 \, \text{Pa} \cdot 5 \, \text{m}^2 = 1000 \, \text{N}
\]
#### Answer:
\[
\boxed{1000 \, \text{N}}
\]
---
Problem 3:
A tractor has tyres of area 3 m². It has a weight of 12,000 N. What pressure does the tractor put on the ground?
#### Solution:
We are given:
- \( F = 12,000 \, \text{N} \)
- \( A = 3 \, \text{m}^2 \)
We need to find the pressure \( P \). Use the pressure formula:
\[
P = \frac{F}{A}
\]
Substitute the given values:
\[
P = \frac{12,000 \, \text{N}}{3 \, \text{m}^2} = 4,000 \, \text{Pa}
\]
#### Answer:
\[
\boxed{4,000 \, \text{Pa}}
\]
---
Problem 4:
A truck has tyres of area 5 m². It puts a pressure of 15,000 N/m² on the road. What is the weight of the truck?
#### Solution:
We are given:
- \( P = 15,000 \, \text{N/m}^2 \)
- \( A = 5 \, \text{m}^2 \)
We need to find the force \( F \), which represents the weight of the truck. Rearrange the pressure formula to solve for \( F \):
\[
F = P \cdot A
\]
Substitute the given values:
\[
F = 15,000 \, \text{N/m}^2 \cdot 5 \, \text{m}^2 = 75,000 \, \text{N}
\]
#### Answer:
\[
\boxed{75,000 \, \text{N}}
\]
---
Final Answers:
1. \(\boxed{75 \, \text{m}^2}\)
2. \(\boxed{1000 \, \text{N}}\)
3. \(\boxed{4,000 \, \text{Pa}}\)
4. \(\boxed{75,000 \, \text{N}}\)
Parent Tip: Review the logic above to help your child master the concept of pressure force area worksheet.
