← Friction and forces in two dimensions

Draw the free-body diagrams of a connected pair

A tow rope accelerates two crates joined by a cord: June's rope attaches to the front crate, and the cord runs back to the rear crate.

One picture of the whole pair cannot answer questions about the cord. For that, you draw each crate alone.

The rule that decides what goes on each drawing is the one every free-body diagram obeys: only the forces acting ON that object.

Draw one free-body diagram per object. Each diagram shows only the forces acting on its own object.

Here is the front crate's diagram. The rope acts on it: a forward force. The cord acts on it too: a backward force, toward the rear crate. That backward force is the cord's tension, T.

rope forceT (cord)
The front crate's diagram: the rope's force on it points forward, and the cord's tension on it points backward. Only the horizontal forces are drawn.

Here is the rear crate's diagram. The rope does not touch the rear crate, so the rope's force appears nowhere on this diagram.

The cord does act on the rear crate, with a forward force. So the cord's tension T appears on this diagram as well, pointing forward.

T (cord)
The rear crate's diagram: the cord's tension on it points forward, and the rope appears nowhere. Only the horizontal forces are drawn.

One cord, two diagrams: the cord joins both crates, so its tension appears on both, pointing opposite ways, from each crate toward the cord's other end.

Each diagram also carries its own weight and normal force, drawn as always. The panels above show only the horizontal forces, where the new rule lives.

A cord joins two wagons, and a tow rope attaches to the front wagon. On which free-body diagrams does the cord's tension appear?

A cord joins two wagons being towed forward. On the REAR wagon's free-body diagram, which way does the cord's tension point?

A tow rope attaches to the front wagon of a cord-joined pair. On which free-body diagrams does the tow rope's force appear?

One free-body diagram per object, each carrying only the forces acting on its own object. A connecting cord's tension appears on both diagrams, pointing from each object toward the cord's other end.

A cord joins two sleds, and a snowmobile's tow line attaches to the front sled. State where the tow line's force and the cord's tension appear on the two free-body diagrams.

The tow line touches only the front sled.

So the tow line's force appears only on the front sled's diagram, pointing forward.

The cord joins both sleds.

So the cord's tension appears on both diagrams: backward on the front sled's, forward on the rear sled's.

The tow line's force appears only on the front sled's diagram. The cord's tension appears on both diagrams, pointing opposite ways.

A worker's crate is pushed from behind and pushes a second crate ahead of it, staying in contact. State which horizontal contact forces appear on the FRONT crate's diagram.

Only forces acting on the front crate belong on its diagram.

The rear crate touches it, so the rear crate's contact force appears, pointing forward.

The worker touches only the rear crate, so the worker's applied force appears nowhere on the front crate's diagram.

Only the rear crate's forward contact force, plus the front crate's own weight and normal force.

Your turn

The figure shows the two free-body diagrams drawn for a cord-joined pair of boxes towed by a rope attached to the front box. Only the horizontal forces are drawn. Which statement describes the diagrams?

front box's diagramrope forceTrear box's diagramrope force

A crate is pushed from behind and pushes a second crate ahead of it, staying in contact. Which horizontal force appears on the FRONT crate's free-body diagram?

Why must the cord's tension be drawn on BOTH diagrams of a cord-joined pair?