Lesson overview

Resultant force: What does an unbalanced force do to a moving object?

Float a puck on an air table and pull it with force meters: balance the pulls and it stays still or glides steadily in a straight line; unbalance them and it speeds up, slows down or curves. Then pull east and north at once and find the resultant by scale drawing and by calculation, measure how the acceleration depends on the force and the mass, and send the puck round a pin on a string to find what keeps it in a circle.

Suggested sequence

Lesson 1 · Balanced and unbalanced forces. Forces as arrows and free-body diagrams; the resultant of forces along one line; balanced forces leave an object at rest or moving steadily in a straight line, and an unbalanced force changes its speed or its direction. Read together (10–15 min), show or explore the experiment (10 min), practise with self-checking (15–20 min).
Lesson 2 · Scalars, vectors and resultants. Supplement: scalars and vectors; speed and velocity, mass and weight; the resultant of two forces or velocities at right angles, by scale drawing and by calculation. Read together (10–15 min), show or explore the experiment (10 min), practise with self-checking (15–20 min).
Lesson 3 · F = ma and circular motion. Supplement: resultant force = mass × acceleration, with the acceleration in the direction of the force; motion in a circle needs a force towards the centre, bigger for a faster speed, a smaller circle or a bigger mass. Read together (10–15 min), show or explore the experiment (10 min), practise with self-checking (15–20 min).
End of module · final check. 2 new questions, 20–30 min, without hints or notes; pupils check their answers once they have answered them all.
One to two weeks later · return questions. 2 questions, 15 min, lesson closed.

Learning goals

Part 1: Balanced and unbalanced forces

Determine the resultant of two or more forces acting along the same straight line (1.5.1.3)
Know that an object either remains at rest or continues in a straight line at constant speed unless acted on by a resultant force (1.5.1.4)
State that a resultant force may change the velocity of an object by changing its direction of motion or its speed (1.5.1.5)

Part 2: Scalars, vectors and resultants

Supplement: understand that a scalar quantity has magnitude (size) only and that a vector quantity has magnitude and direction (1.1.4)
Supplement: know that the following quantities are scalars: distance, speed, time, mass, energy and temperature (1.1.5)
Supplement: know that the following quantities are vectors: force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength (1.1.6)
Supplement: determine, by calculation or graphically, the resultant of two vectors at right angles, limited to forces or velocities only (1.1.7)

Part 3: F = ma and circular motion

Supplement: understand that a scalar quantity has magnitude (size) only and that a vector quantity has magnitude and direction (1.1.4)
Supplement: know that the following quantities are scalars: distance, speed, time, mass, energy and temperature (1.1.5)
Supplement: know that the following quantities are vectors: force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength (1.1.6)
Supplement: determine, by calculation or graphically, the resultant of two vectors at right angles, limited to forces or velocities only (1.1.7)
Supplement: recall and use the equation F = ma and know that the resultant force and the acceleration are in the same direction (1.5.1.11)
Supplement: describe, qualitatively, motion in a circular path due to a force perpendicular to the motion: (a) speed increases if force increases, with mass and radius constant; (b) radius decreases if force increases, with mass and speed constant; (c) an increased mass requires an increased force to keep speed and radius constant (1.5.1.12)

Misconceptions to listen for

“a: 0.50 N east: add the two pulls.” — Only forces in the same direction add up. These two pull opposite ways, so subtract: 0.35 N − 0.15 N.
“c: 0.20 N west.” — The size is right, but the resultant points the same way as the bigger pull, and the bigger pull, 0.35 N, is towards the east.
“d: 0.25 N east, halfway between the two pulls.” — The resultant is not an average. It is the single force with the same effect as both: subtract the opposite forces, 0.35 N − 0.15 N.
“The resultant is 0.75 N, because there are three forces to add.” — Only the forces in the same direction add. The 0.40 N points the other way, so it takes away: 0.25 + 0.10 − 0.40.
“The resultant points east, because two of the three forces point east.” — The number of arrows does not decide the direction; their sizes do. East has 0.35 N in all, west has 0.40 N, so the resultant points west.
“Moving east with zero resultant: it slows down and stops.” — With no resultant force, nothing changes its velocity. On the air table the gaps between the dots stayed equal, 2 cm every 0.1 s, all the way across.
“Moving east with a resultant towards the west: it stops at once.” — A force changes the velocity gradually. In run 4 the puck took 0.6 s to stop, and went 9 cm further, before it came back.
“Moving east with a resultant towards the north: it turns and goes straight north at once.” — The path curves gradually. In run 5 the puck curved north more and more, and it was still moving east as well when it reached the rim.
“a: The force of the nudge stays in the puck and keeps it going.” — A force acts only while something pushes or pulls. Once the hand let go, the nudge was over. The puck keeps going because nothing changes its velocity.
“c: Meter W pulls it along, because the puck moves towards it.” — Meter W pulls 0.10 N west and meter E pulls 0.10 N east. They balance, so together they have no effect on the motion.

Scope

Scalars have size only and vectors have size and direction (1.1.4); distance, speed, time, mass, energy and temperature are scalars (1.1.5); force, weight, velocity, acceleration, momentum, electric field strength and gravitational field strength are vectors (1.1.6); the resultant of two vectors at right angles, by scale drawing and by calculation, for forces and velocities only (1.1.7); the resultant of two or more forces along the same straight line (1.5.1.3); with no resultant force an object stays at rest or moves in a straight line at constant speed (1.5.1.4); a resultant force changes the velocity of an object by changing its speed or its direction of motion (1.5.1.5); F = ma, with the force and the acceleration in the same direction (1.5.1.11); motion in a circular path due to a force at right angles to the motion: with the mass and the radius constant, a bigger force goes with a bigger speed; with the mass and the speed constant, a bigger force goes with a smaller radius; with the speed and the radius constant, a bigger mass needs a bigger force (1.5.1.12). 1.1.4–7, 1.5.1.11 and 1.5.1.12 are Supplement. F = mv²/r is not required and is not used. Springs are in Stretching springs, friction and drag in Acceleration, falling and drag, moments in Moments and balance, and momentum in Momentum and collisions.

Open the first part as pupils see it