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Acceleration is net force divided by mass

Years 9–12Stage 5 to Stage 6Run it

Newton's second law: double the net force on the same mass and the acceleration doubles; double the mass and it halves.

Demonstration: a simplified modelNot to scale1 · Release

A cart on a level track is joined by a string over a pulley to a hanger of slotted masses. Hanging mass 0.05 kg, cart 0.95 kg, friction limit 0.00 N. The string pulls the cart forward with 0.47 N and pulls the hanger up just as hard, less than the hanger's weight of 0.49 N, so the hanger is sped up too. Along the string the net force is 0.49 N on 1.00 kg, so the acceleration is 0.49 m/s². At 0.00 s the cart has moved 0.00 m and its velocity is 0.00 m/s.

The hanger's weight pulls the cart and the hanger along together, so both masses are being accelerated.

  1. Cart
  2. Hanger
  3. Front of the cart every 0.2 s

Key Arrows are forces, to one scale: the string's pull forward and up (amber), weight down (blue), friction back (red). Dashed: the starting run, or a slack string.

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The idea, step by step

Not to scale

  1. A cart on a level track is joined by a string over a pulley to a hanger of slotted masses. Hanging mass 0.10 kg, cart 0.30 kg, friction limit 0.00 N. The string pulls the cart forward with 0.74 N and pulls the hanger up just as hard, less than the hanger's weight of 0.98 N, so the hanger is sped up too. Along the string the net force is 0.98 N on 0.40 kg, so the acceleration is 2.45 m/s². At 0.40 s the cart has moved 0.20 m and its velocity is 0.98 m/s.
    2 · The string's pullHeavy hanger, light cart: the string pulls the cart less hard than the hanger's weight, because the weight also speeds up the hanger.1 Cart · 2 Hanger · 3 Front of the cart every 0.2 s
  2. A cart on a level track is joined by a string over a pulley to a hanger of slotted masses. Hanging mass 0.10 kg, cart 0.90 kg, friction limit 0.00 N. The string pulls the cart forward with 0.88 N and pulls the hanger up just as hard, less than the hanger's weight of 0.98 N, so the hanger is sped up too. Along the string the net force is 0.98 N on 1.00 kg, so the acceleration is 0.98 m/s². At 0.90 s the cart has moved 0.40 m and its velocity is 0.88 m/s.
    3 · Twice the forceFrom the start (dashed), move 0.05 kg from the cart to the hanger: twice the net force, the same total mass, twice the acceleration.1 Cart · 2 Hanger · 3 Front of the cart every 0.2 s
  3. A cart on a level track is joined by a string over a pulley to a hanger of slotted masses. Hanging mass 0.10 kg, cart 0.95 kg, friction limit 0.00 N. The string pulls the cart forward with 0.89 N and pulls the hanger up just as hard, less than the hanger's weight of 0.98 N, so the hanger is sped up too. Along the string the net force is 0.98 N on 1.05 kg, so the acceleration is 0.93 m/s². At 0.90 s the cart has moved 0.38 m and its velocity is 0.84 m/s.
    4 · More on the hangerFrom the start (dashed), double the hanging mass: twice the net force, but the added mass speeds up too: 0.93 m/s², less than twice 0.49.1 Cart · 2 Hanger · 3 Front of the cart every 0.2 s
  4. A cart on a level track is joined by a string over a pulley to a hanger of slotted masses. Hanging mass 0.05 kg, cart 1.95 kg, friction limit 0.00 N. The string pulls the cart forward with 0.48 N and pulls the hanger up just as hard, less than the hanger's weight of 0.49 N, so the hanger is sped up too. Along the string the net force is 0.49 N on 2.00 kg, so the acceleration is 0.25 m/s². At 1.20 s the cart has moved 0.18 m and its velocity is 0.29 m/s.
    5 · Twice the massLoad the cart until the total mass doubles: the same net force now gives half the acceleration.1 Cart · 2 Hanger · 3 Front of the cart every 0.2 s
  5. A cart on a level track is joined by a string over a pulley to a hanger of slotted masses. Hanging mass 0.02 kg, cart 0.95 kg, friction limit 0.20 N. Friction holds the cart still: the string pulls the cart forward with 0.20 N, the hanger's whole weight, and friction pulls it back as hard, so the net force is 0.00 N and nothing moves. At 1.20 s the cart has moved 0.00 m.
    6 · Held stillFriction can hold the hanger's weight, so on each body the two forces are equal and opposite: no net force, no motion.1 Cart · 2 Hanger · 3 Front of the cart every 0.2 s
  6. A cart on a level track was pulled by a string over a pulley by a hanger of slotted masses. Hanging mass 0.05 kg, cart 0.95 kg, friction limit 0.00 N. The hanger has landed and the string is slack, so it pulls nothing. On the cart alone friction is 0.00 N, so the net force is 0.00 N on 0.95 kg and the acceleration is 0.00 m/s². At 2.00 s the cart has moved 0.90 m and its velocity is 0.70 m/s.
    7 · LandedWhile the hanger pulls, a steady net force: the line rises straight, the dots spread. After landing, no net force: a flat line, even dots.1 Cart · 2 Hanger · 3 Front of the cart every 0.2 s

The cart's motion at equal steps of time: one row for each dot on the track, then the latest time if it falls between dots

Time since release (s)Distance moved (m)Velocity (m/s)Velocity gained since the row above (m/s)
0.000.0000.00
0.200.0100.100.10
0.400.0390.200.10
0.600.0880.290.10
0.800.1570.390.10
1.000.2450.490.10
1.200.3530.590.10
1.400.4810.690.10
1.600.6200.700.01
1.800.7600.700.00
2.000.9000.700.00
2.151.0000.00

Try it in the Lab

Practicals with real materials, each with its safety card.

With a learner

Three questions to ask

  1. What pulls the cart along, and what holds it back?
  2. Why does the cart speed up faster when a mass moves from the cart to the hanger?
  3. What does the cart do after the hanger lands, and why?

What to expect

Many learners expect the cart to settle at a steady speed while the hanger is still pulling.

What to try next

Open a practical in Try it in the Lab, above, to time a real trolley with light gates or a ticker timer.

About this model

What is simplified

  • The string and pulley are light and the pulley turns freely, so the string only turns the hanger's pull round the corner.
  • Friction holds a still cart with whatever force it needs, up to the limit you choose; on a rolling cart it is that limit. A real cart's friction changes a little with speed and load.
  • The cart's weight and the track's push up on it balance, so they are not drawn. The forces along the track and the string are drawn on the body they act on, all to one scale; the cart's are drawn along its middle.
  • The hanger lands on a box on the floor. Once it rests there, the box holds it up and the forces on it are not drawn.
  • Distances along the track and the hanger's drop are drawn to one scale. The cart, wheels, pulley and masses are drawn larger so they can be seen.
  • Each disc on the hanger stands for one step of the hanging-mass slider, the hanger's own mass included.
  • Air resistance is left out. The run is shown in real time, and the clock stops at the end of the time slider even if the cart is still rolling.

Numbers and their sources

Review

Demonstration: a simplified model. Checked against its written sources, 26 September 2026. Not reviewed by a qualified teacher.

Curriculum references

SC5-WAM-02PH11-9PY-11-01AC9S10U05

Reference, not a verified alignment.

All demonstrations Practicals in the Lab