Physics Problem- Two Blocks with Mass and Volume

Two Blocks with Mass and Volume: The Physics Problem You Actually Need to Master

Every physics student encounters this problem eventually. Two blocks, different masses, different volumes, sitting on a surface or submerged in fluid. The question changes depending on what your professor wants, but the core concepts never do.

This guide cuts through the confusion. Here's how to solve any variation of this problem.

What the Problem Actually Gives You

Most versions of this problem provide:

• Mass of Block A and Block B
• Volume of Block A and Block B
• Sometimes density of a fluid they're placed in
• Sometimes a surface they're resting on

The question then asks you to find something like density, weight, normal force, whether they sink or float, or net force on the system.

The Formulas You Need Memorized

Stop looking these up every time. Write them down once and own them:

• Density: ρ = m/V
• Weight: W = mg (g = 9.8 m/s² on Earth)
• Normal Force (flat surface, at rest): N = mg
• Buoyant Force: F_b = ρ_fluid × V_submerged × g
• Net Force: F_net = ma
• Friction: F_f = μN

Example Problem with Full Solution

The Setup

Block A: mass = 4 kg, volume = 0.002 m³
Block B: mass = 2 kg, volume = 0.001 m³
Question 1: Find the density of each block
Question 2: Find the weight of each block
Question 3: Both blocks sit on a table. Find the normal force on each

Solution: Density First

Block A density = 4 kg / 0.002 m³ = 2000 kg/m³
Block B density = 2 kg / 0.001 m³ = 2000 kg/m³

Interesting. Same density. This happens when mass and volume scale proportionally.

Solution: Weight

Block A weight = 4 kg × 9.8 m/s² = 39.2 N
Block B weight = 2 kg × 9.8 m/s² = 19.6 N

Solution: Normal Force

On a flat horizontal surface with no vertical acceleration, normal force equals weight.

Block A: N = 39.2 N
Block B: N = 19.6 N

That's it. The table pushes up with exactly enough force to support each block.

Harder Variation: Blocks in Fluid

This is where students lose marks. The problem puts one or both blocks in water (ρ_water = 1000 kg/m³) and asks whether they sink or float, or what the apparent weight is.

New Setup

Block A: mass = 3 kg, volume = 0.002 m³
Block B: mass = 1.5 kg, volume = 0.001 m³
Both blocks are dropped into water. What happens?

Step 1: Find Density of Each

Block A: 3 / 0.002 = 1500 kg/m³
Block B: 1.5 / 0.001 = 1500 kg/m³

Step 2: Compare to Water

Both blocks have density of 1500 kg/m³. Water is 1000 kg/m³.

1500 > 1000, so both sink.

Step 3: Buoyant Force (if asked)

Buoyant force = ρ_water × V_block × g
F_b = 1000 × 0.002 × 9.8 = 19.6 N for Block A

Weight of Block A = 3 × 9.8 = 29.4 N

Apparent weight = Weight - Buoyant force
Apparent weight = 29.4 - 19.6 = 9.8 N

Comparison: Both Blocks Side by Side

Why Your Answer Might Be Wrong

• Confusing mass with weight. Mass is kg. Weight is Newtons. Use the right units.
• Forgetting g. Weight requires multiplication by 9.8 m/s². Density does not.
• Using total volume instead of submerged volume. When partially submerged, only the displaced volume counts for buoyant force.
• Forgetting that normal force changes in fluids. In air, N = mg. In fluid, N = mg - F_b.

Quick Reference: Decision Tree

When you see "two blocks in fluid" problems, run through this:

1. Find density of each block (m/V)
2. Compare block density to fluid density
3. If block density > fluid density → sinks
4. If block density < fluid density → floats (partially submerged)
5. If block density = fluid density → neutral buoyancy

The Takeaway

These problems test the same three concepts over and over: density, weight, and buoyant force. Once you can calculate those three things reliably, every variation of this problem becomes solvable. The numbers change. The method doesn't.