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Block on block problems
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Friction between stacked blocks sets maximum common acceleration.
For stacked blocks, friction between them provides the top block's acceleration, limited by μₛ m g. The top block slips when the common acceleration needed exceeds μₛg.
Top 2 kg, bottom 4 kg, μₛ = 0.5: the maximum shared acceleration is 4.9 m/s².
Analyse each block separately; friction pairs are equal and opposite.
In more detail
In block-on-block problems, the friction between the blocks, and between the lower block and the surface, act in opposite directions. Each block requires its own free-body diagram.
Real-world uses
- Stacked loads on a truck can slide relative to each other, and engineers check the friction between them.
- Physics exams use block problems to test understanding of contact forces.
- Stacked crates on a moving truck can slide if the top crate's friction limit is exceeded, so drivers accelerate gently.
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Frequently asked questions
Why draw separate diagrams for each block?
Because each block experiences different forces, and their accelerations may differ.
Can the top block slide on the bottom one?
Yes, if the applied force exceeds the maximum static friction between them.
What limits the acceleration of a stack of blocks?
The largest acceleration the lower block can give the top block without slipping, given the friction coefficient between them.
Related topics in Newton's Laws & Forces
Angle of friction and repose · Rolling friction · Friction on inclines with applied force · Impulse · Linear momentum · Second law as rate of momentum change