Resultant Forces

Activities to try

1. 1

   Force-arrow playground: balanced forces that keep gliding

   Why it works: A zero resultant means no change in motion — which includes continuing to move at a steady speed, not only being at rest. A sustained unbalanced resultant keeps changing the motion; when it points along the direction of travel the speed keeps climbing, showing that force governs CHANGE of motion rather than speed itself. The resultant is the single equivalent of the combined forces, and for non-collinear forces it is found by head-to-tail (vector) addition. This model assumes negligible horizontal friction, so the drawn arrows are the only horizontal forces.

   1. Set the crate moving steadily to the right. In this model horizontal friction is treated as negligible, so the only horizontal forces acting are the arrows you draw.
   2. On the already-moving crate, place two equal and opposite horizontal force arrows and adjust their lengths so they are exactly balanced (zero resultant).
   3. Predict what the already-moving crate will do BEFORE releasing: will it stop, slow down, or keep moving at the same speed? State your reasoning.
   4. Observe the crate: with balanced forces (zero resultant) it keeps gliding to the right at a steady speed rather than stopping.
   5. Now make the RIGHTWARD arrow longer than the leftward one, so the resultant points right — the same direction the crate is already moving — and watch it accelerate; keep that arrow stretched and notice its SPEED keeps climbing for as long as the unbalanced force acts along the motion.
2. 2

   Combining forces and judging the direction of change

   Why it works: Collinear forces combine by signed addition along the line; non-collinear forces need head-to-tail construction. The resultant points in the direction of the CHANGE in motion — which can be opposite to the current direction of travel when an object is slowing down. A zero resultant does not mean there are no forces; it means the forces balance.

   1. Drag arrows head-to-tail (or along a number line for collinear cases) to construct the resultant, then draw or state its direction and size.
   2. For collinear forces, calculate the resultant: e.g. 30 N right and 20 N left gives 10 N to the right.
   3. Answer multiple-choice items on which way the resultant points for an object that is stated to be speeding up, slowing down, or turning, and justify the choice from the stated initial motion.
   4. Categorise described situations as balanced (zero resultant, no change in motion) or unbalanced (non-zero resultant, motion changes).
   5. Decide whether a zero resultant means there are no forces on the object, and explain.
3. 3

   Tug-of-war predict–observe–explain

   Why it works: Large equal and opposite pulls still give a zero resultant; the size of the individual forces does not add up to a 'big leftover'. A zero resultant means no change in motion, so a steadily falling skydiver has a zero resultant yet is still moving, and a forwards-moving braking car has a backward resultant while still moving forwards.

   1. Set up two students to pull a rope tied to a central marker; they will both pull hard and adjust until the marker holds still.
   2. Before the pulling starts, predict: if both students pull hard and the marker is held still, what is the resultant on the marker? Does a big pull on each side mean a big resultant? Say WHY.
   3. Observe that the marker can be held still even under large pulls, then explain in terms of the resultant why, while it stays still, the two pulls must be equal and opposite.
   4. Discuss the skydiver case: during a steady (terminal-velocity) fall, state the resultant and whether she is moving.
   5. Discuss a braking car that is still moving forwards: state which way the resultant points and why.