PHYS 1021 Problem Set 3 – Step-by-Step Physics Guidance

Q4. What weight of water must be poured into the tube in order to burst the barrel?

Background

Topic: Fluid Statics & Pascal's Principle

This question tests your understanding of how pressure is transmitted in fluids and how a small amount of water in a narrow tube can exert a large force on the top of a barrel due to the height of the water column.

Key Terms and Formulas

• Pressure due to a fluid column: $P = \rho g h$

• Force from pressure: $F = P \times A$

• Where:

  • $\rho$ = density of water ($1000\ \mathrm{kg/m^3}$)

  • $g$ = acceleration due to gravity ($9.81\ \mathrm{m/s^2}$)

  • $h$ = height of water column in the tube

  • $A$ = area of the barrel's top ($A = \pi r^2$)

Step-by-Step Guidance

1. Calculate the area of the barrel's top using its diameter ($d = 75\ \mathrm{cm} = 0.75\ \mathrm{m}$): $A = \pi \left(\frac{d}{2}\right)^2$

2. Set the force required to burst the barrel equal to the force exerted by the water column: $F = P \times A = \rho g h \times A$

3. Solve for the height $h$ of the water column needed to produce the bursting force: $h = \frac{F}{\rho g A}$

4. Calculate the volume of water in the tube using the tube's diameter ($d_{tube} = 1.0\ \mathrm{cm} = 0.01\ \mathrm{m}$): $V = A_{tube} \times h = \pi \left(\frac{d_{tube}}{2}\right)^2 \times h$

5. Find the weight of water by multiplying the volume by the density and gravity: $W = \rho \times V \times g$

Try solving on your own before revealing the answer!

Final Answer: 0.11 N

The weight of water required is very small because the pressure from the tall column of water in the narrow tube is transmitted to the large area of the barrel's top, demonstrating Pascal's Principle.