Choose how the blocks are joined at the top: ① touching (pushed) · ② strings (pulled) · ③ a tow bar (it can pull
and push) · ④ mixed: a string from A to B, and B touches C · ⑤ stacked: B on top of A (and C on top of B).
Pick an example (cards, problem set, slides, Smart Cart demo) or set your own: 2 or 3 blocks, the masses, the force F, its
angle θ, where it acts (push or pull, left or right end, or the middle block) and the surface. Use ▼ ▲ next to a box or type a value.
Press ▶ Go. ◂ / ▸ (or the ← → keys) step through the motion. While the blocks move, press ✋ Let go (only friction
acts) or ◀ Brake (a braking force of size F on the block you pushed or pulled).
= const. v sets the force that keeps the blocks moving at a constant velocity: the resultant force on every block is zero —
but the forces between the blocks are still there.
In the scene, each 3rd-law pair has its own colour: the force of A on B and the force of B on A are drawn on the two different blocks,
equal in size and opposite in direction.
The middle column shows the free-body diagram of every block (to scale) and of the whole system, where the forces between the
blocks cancel. The table lists every horizontal force and checks ΣF = ma for each block.
● Record (Data tab) saves the values at this instant. The Data tab plots a against F (gradient = 1 / total mass) and the force
between two blocks against F (gradient = the fraction of the mass that it moves).
Work through the Tasks tab. Write explanations on your worksheet.
The physics
Newton's 3rd law: if A pushes (or pulls) B, then B pushes (or pulls) A with a force of the same size, in the opposite direction,
of the same type. The two forces act on different bodies, so they never cancel on one body. This is true at every instant —
accelerating, at constant velocity, slowing down or at rest.
Whole system: a = (F cos θ − ΣFf) / (mA + mB + …)
The forces between the blocks are internal: they come in 3rd-law pairs and cancel for the whole system. To find one, draw the FBD of
the blocks beyond it: e.g. pushing A, the contact force on B is FA on B = mBa + Ff,B.
Without friction (or with the same μ for every block) the force between two blocks is the fraction of F that matches the mass it
has to move: FA on B = F × mB / (mA + mB). Push the other end and it changes.
A string can only pull (it goes slack if the blocks move closer). Touching blocks can only push (they separate if the front one is
faster). A tow bar or rod can pull (tension) and push (compression).
Stacked blocks: friction is the only horizontal force between them. Pull the bottom block and friction from A drags B forwards — and
B pulls A back with the same friction (a 3rd-law pair). B moves with A as long as it needs less than μsFN, so amax = μsg;
pull harder and B slides back on A. Vertically, B pushes down on A with the same normal force with which A pushes B up. Each lower block has a
raised stop at both ends (the truck's cab).
A force at an angle θ: only F cos θ acts along the floor. Pulling up (sin θ) makes FN and friction smaller on that block;
pushing down makes them bigger.
Model: g = 9.81 N kg⁻¹; light, inextensible strings; rigid blocks; sliding friction μdFN (or a fixed resistive force)
against the motion, static friction up to μsFN (μ per block: μs = μd). At rest, static friction is taken up first by the
block nearest to the force. When blocks hit or a string jerks tight they move on together (momentum is conserved). The braking force is horizontal; with stacked blocks it acts on the bottom block.