How Forces Affect Motion
Why does a canoe move forward when its paddle pushes water backward? Why does a heavier cart need a stronger push? Discover the answers by predicting, experimenting and explaining.
Use each lesson’s completion checkbox when you can explain its key idea.
Force: strength and direction both matter
A force is a push or a pull arising from an interaction between objects. It can start motion, change speed or direction, or change shape. A kicked football, a struck cricket ball and a squeezed lemon illustrate these effects.
The strength of the force. The SI unit is the newton, symbol N. Write “newton” with a small n.
“20 N to the right” is a complete description. Force is a vector: a change in direction can change its effect.
A spring balance measures force through the stretch of its spring. When used to weigh an object, it measures the object’s gravitational force, rather than its mass.
Experiment 1 · Apply a force
∿∿∿∿∿ 40 N
An arrow represents force, not velocity. A force can exist without visible movement if another force balances it.
Pause & predict
Which description gives both the magnitude and direction of a force?
Balanced and unbalanced forces
Most objects experience several forces. The net force is their vector sum. For forces along one straight line, choose right as positive.
Opposite directions: subtract magnitudes; the net force points towards the stronger force.
Balanced: net force = 0 N.
A floating ball has upward buoyancy balancing its downward weight. A barbell held steady has an upward support force balancing its weight. A moving object can also have balanced forces.
Experiment 2 · Combine two forces
The box position indicates the net-force direction; this is a force visualisation, not a motion prediction.
Worked example · 10 N and 6 N
Both right: 16 N right. Opposite, with 10 N right: 4 N right. Opposite, with 10 N left: 4 N left.
Pause & predict
A box moves at constant velocity. Which statement is correct?
Friction: investigate the surfaces
Sliding friction opposes relative sliding between surfaces. A sliding object slows after the push ends because friction continues to act. Static friction can prevent an object from starting to slide; it adjusts to the applied force up to a limiting value.
Tape four coins together. Launch them using the same rubber-band stretch on level surfaces. Measure the travel distance and repeat each trial. Keep the starting conditions as similar as possible.
Pull a block across each surface. At constant speed, the horizontal pulling force equals sliding friction. The reading just before movement instead estimates limiting static friction.
Weight acts downwards; the surface’s normal force acts upwards. On a level surface with no other vertical force and no vertical acceleration, these balance.
Experiment 3 · Launch a sliding block
Choose an initial speed and a friction model. Compare the stopping time and distance.
Constant deceleration model. One common scale is used for every surface; long journeys continue beyond the displayed track.
Can your push overcome static friction?
Simplified model: maximum static friction = 50 N; sliding friction = 50 N. It illustrates the textbook example, not a universal friction rule.
Friction is also helpful: the ground’s friction on your foot can point forwards as you walk. It opposes slipping at the contact, not necessarily the motion of your whole body.
Pause & predict
A sliding block is released with the same initial speed on two level surfaces. Greater sliding friction gives…
Newton’s first law: motion does not need a net force
Inertia is resistance to a change in velocity; mass measures inertia. When a bus brakes, your body tends to retain its forward velocity. A seat belt provides the force needed to slow you.
Galileo’s thought experiment removed the impediments to motion: without friction or another net force, a moving object would keep moving. Newton formalised this idea in his first law.
Experiment 4 · Read two graphs together
Think it through · A person keeps pushing a moving box
If the forward push exactly balances friction, the net force is zero and the box continues at constant velocity. The push counters friction; it does not create acceleration.
Pause & predict
On an ideal frictionless level surface, a ball already moving needs what to keep the same velocity?
Newton’s second law: force changes velocity
Acceleration points in the direction of the net force. At fixed mass, a larger net force gives a larger acceleration. At fixed net force, a larger mass gives a smaller acceleration.
1 N = 1 kg m/s²: one newton gives a 1 kg object an acceleration of 1 m/s². Always use the net force, not just one of the applied forces.
Experiment 5 · Force, mass and acceleration
Starts from rest on an ideal frictionless track. Positive is right. Changing a setting resets the trial.
A cart is pulled by a thread over a pulley attached to a hanging cup. Add load to the cup and compare the times for the same travel distance from rest.
Keep the hanging load the same, add mass to the cart, and compare the travel times. The heavier system generally accelerates less.
These are teacher-led demonstrations. In an ideal cart–hanging-load system, a = mhg/(mcart + mh); the thread’s pull on the cart is not simply the full hanging weight. Use measured times to estimate acceleration. Friction and measurement errors affect real results.
Analyse your timed cart experiment
Assumes each trial starts from rest and has constant acceleration: a = 2s/t².
Weight is a force
Near Earth’s surface, W = mg, with g ≈ 9.8 m/s². Mass is measured in kg; weight in N. Neglecting air resistance, falling objects have the same gravitational acceleration regardless of mass.
Worked example · The steady barbell
Two 10 kg weights and a 10 kg bar have total mass 30 kg. Weight = 30 × 9.8 = 294 N downwards. The weightlifter applies 294 N upwards to hold it steady.
Pause & predict
A constant net force gives a 4 kg cart acceleration 3 m/s². For an 8 kg cart under the same net force, acceleration is…
Stopping safely and finding force from graphs
A fielder moves their hands backwards while catching a ball. Bubble wrap, landing mats and airbags also increase the time over which motion stops. For the same mass and change in velocity, a longer stopping time reduces the average net stopping force.
A coconut stopped abruptly by a hard surface experiences a large force over a short time. In a vehicle, airbags work together with seat belts.
Experiment 6 · Catch the ball gently
The calculation gives average net force on the ball. Actual contact force depends on other forces too.
Experiment 7 · Sports-car graph
A 1500 kg car moves east. Select one segment of its velocity–time graph.
The slope of a velocity–time graph gives acceleration. A horizontal segment means zero net force; it does not prove that all individual forces are absent.
Pause & predict
The same ball is stopped in twice the time. Its average net stopping force is…
Newton’s third law: equal forces on different objects
The two forces act on different objects. They therefore do not balance each other in the force calculation for either object. They occur at the same time; “reaction” does not mean a delayed response.
With teacher supervision, push a heavy table while seated on a wheeled chair with feet off the floor. The table pushes you and the chair in the opposite direction.
Connect two identical balances hook to hook and pull while they remain steady. Both read the same tension. A 10 N pull does not make either read 20 N.
Experiment 8 · Two spring balances
10 N
10 N
Identify the interaction pair
Experiment 9 · Equal force, unequal acceleration
Two model carts repel each other on a frictionless track. Each receives the same force magnitude for one second.
Worked example · Why Earth’s movement is not visible
A fruit and Earth exert equal gravitational forces on each other. Since a = F/m and Earth’s mass is enormous, its acceleration is extremely small. Equal force does not imply equal acceleration.
Worked example · Bullet and gun
For the textbook’s illustrative values, force magnitude = 2 N on both objects. Bullet: a = 2/0.1 = 20 m/s². Gun: a = 2/5 = 0.4 m/s² in the opposite direction. These are illustrative values, not typical firearm data.
Pause & predict
A loaded cart collides with an empty cart. During the collision…
Balloon propulsion, rocket lift-off and braking in space
Activity 6.7: Tape a straw to an inflated balloon, pass a taut thread through the straw and release the balloon’s neck. Air leaves one way; the balloon moves the other way. Use teacher supervision for the setup.
A rocket pushes exhaust gas downwards; the gas pushes the rocket upwards. The rocket can lift off when its thrust exceeds its weight. It does not need to push on air, so rocket propulsion also works in space.
To slow a spacecraft, direct its exhaust ahead of its motion. The resulting thrust acts backwards. Changing the exhaust direction changes the thrust direction.
Balloon-on-a-thread demonstration
Direction demonstration; the animation’s speed is illustrative. A real balloon’s thrust changes as it deflates.
Experiment 10 · Will the model rocket lift off?
Short demonstration with constant mass and thrust, g = 9.8 m/s² and no air resistance. A real rocket loses mass as fuel is consumed. While on the pad, a support force prevents downward motion.
Pause & predict
A rocket’s thrust equals its weight. Once freely airborne, neglecting drag, its acceleration is…
Connected objects: use the whole system
Two boxes of masses m₁ and m₂ are connected by a taut, light string on a frictionless horizontal surface. A force F pulls box 1 to the right. The string gives both boxes a common acceleration.
Box 2: T = m₂a
Box 1: F − T = m₁a
When the boxes and light string are treated as one system, tension is internal: the opposite contributions cancel in the system’s net-force sum. The external pull remains. Vertically, the combined normal force balances the combined weight.
Experiment 11 · Pull two connected boxes
Light, taut, inextensible string; frictionless surface. Equal translation shows the common acceleration.
Worked example · Two boxes, one pull
With m₁ = 5 kg, m₂ = 3 kg and F = 16 N, a = 16/8 = 2 m/s². T = 3 × 2 = 6 N. On box 1, net force = 16 − 6 = 10 N = 5 × 2.
Pause & predict
For a system comprising both boxes and the connecting string, tension is…
Bring the ideas together
| Question | Useful idea |
|---|---|
| Will velocity change? | Find the net external force. |
| How much acceleration? | a = Fnet/m |
| How much weight? | W = mg |
| What is the interaction partner? | Third-law forces act on different objects. |
| Several objects connected? | Choose a system; add its masses and identify external forces. |
A dependable numerical method
- Choose the object or system and a positive direction.
- Convert grams to kg, centimetres to metres, and km/h to m/s.
- List the forces and calculate their signed sum.
- Use a = Fnet/m. If needed, connect it to the motion equations.
- State the unit and direction, then check whether the result makes sense.
Your force calculator
Short worked numericals
A rough patch stops a 2 kg object
Initial velocity = 10 m/s. Opposing forces = 7 N + 3 N = 10 N. Choose the initial direction as positive: a = −10/2 = −5 m/s². Using v² = u² + 2as with v = 0, s = 100/10 = 10 m.
A football gains speed during a kick
108 km/h = 30 m/s. For a 0.4 kg ball starting from rest under an estimated net force 800 N, a = 800/0.4 = 2000 m/s². Contact time = 30/2000 = 0.015 s.
Stopping a bullet inside wood
Mass = 50 g = 0.05 kg; penetration = 50 cm = 0.5 m. With u = 100 m/s and v = 0, a = (0 − 10000)/(2 × 0.5) = −10000 m/s². Net stopping-force magnitude = 0.05 × 10000 = 500 N. Constant acceleration is assumed.
Tap-to-reveal revision cards
Inertia
Resistance to a change in velocity. Mass measures inertia.
Balanced forces
Zero vector sum on the chosen object. It may be at rest or moving with constant velocity.
One newton
1 N = 1 kg m/s².
Action and reaction
Equal, opposite, simultaneous forces on different objects.
Graph slopes
Position–time slope gives velocity. Velocity–time slope gives acceleration.
Mass and weight
Mass: kg. Weight: gravitational force mg, in N.
Momentum: an extension
Momentum p = mv. For a closed system in an inertial frame, the net external force equals the rate of change of its total momentum. Variable-mass subsystems such as a rocket require accounting for the momentum carried by entering or leaving material.
Final challenge · 10 questions
Choose an answer, read the explanation and move to the next question. Your first answer counts towards the score.
The journey beyond
Investigate why rolling is often easier than sliding, why increasing the load changes friction, and how lubricants reduce resistance. For a teacher-led extension, repeat the magnetic toy-car experiment with different masses and compare the opposite movements.
Newton’s laws explain a huge range of everyday motion. Relativity or quantum mechanics is needed in regimes such as speeds near the speed of light, strong gravitational fields and atomic scales.
