How do you do the acceleration required practical?

What does the acceleration practical investigate?

It tests Newton's second law in two parts. The first part looks at how an object's acceleration depends on the force pulling it, with the mass kept the same. The second part looks at how the acceleration depends on the mass, with the force kept the same.

It is a required practical on AQA GCSE Physics and on AQA GCSE Combined Science: Trilogy.

What equipment do you need?

The usual set-up is a trolley on a bench, pulled along by a weight falling over the edge.

• A trolley, and slotted masses to load it
• A pulley clamped to the end of the bench
• String, and a mass hanger with slotted masses
• Two light gates connected to a data logger, and a card fixed on top of the trolley to cut the beams
• A balance, to find the mass of the trolley
• A cushion or box under the hanging masses, and a stop at the end of the runway

What is the method?

You release the trolley from rest again and again, changing one thing each time and measuring the acceleration. Without light gates, you can time the trolley over measured distances with a stopwatch, but the results are much less precise.

• Clamp the pulley to the end of the bench. Tie the string to the trolley, run it over the pulley and hang the mass hanger on the end.
• Place the two light gates along the bench, so the card on the trolley passes through both before the hanging masses reach the floor.
• Put some slotted masses on the trolley and the rest on the hanger.
• Hold the trolley still at a marked start line, then let go without pushing it. Record the acceleration from the data logger.
• Part one: move one mass from the trolley to the hanger and repeat. Keep moving masses across one at a time. The pulling force goes up, but the total mass stays the same.
• Part two: keep the same masses on the hanger and add masses to the trolley one at a time, repeating the run each time.
• Do each run at least twice and work out a mean acceleration.

What are the variables?

Each part changes one thing and measures the acceleration. In part one you change the force. In part two you change the mass.

How do you work out and present the results?

Use F = m a, or a = F ÷ m. The pulling force is the weight of the hanging masses, W = m g, with g = 9.8 N/kg. The mass in F = m a is everything that accelerates: the trolley, anything loaded on it and the hanging masses too. With light gates, each speed is the length of the card divided by the time it blocks the beam. The acceleration is the change in speed divided by the time between the gates: a = (v − u) ÷ t, where u is the speed at the first gate and v the speed at the second.

Worked example: the hanger holds 100 g, so the pulling force is 0.100 × 9.8 = 0.98 N. The trolley, its load and the hanging masses add up to 0.80 kg. The light gates show the speed rising from 0.20 m/s to 0.75 m/s in 0.50 s, so a = (0.75 − 0.20) ÷ 0.50 = 1.1 m/s². F = m a predicts 0.98 ÷ 0.80 = 1.2 m/s² (to 2 significant figures). The measured value is a little lower because friction takes some of the pull.

For part one, plot acceleration (y-axis) against force (x-axis). A straight line through the origin shows acceleration is directly proportional to force. If the line meets the force axis a little to the right of zero, that is friction: a small force is needed before the trolley speeds up at all.

For part two, plot acceleration against mass. You get a curve that falls as the mass goes up, because acceleration is inversely proportional to mass: double the mass and the acceleration halves. Plotting acceleration against 1 ÷ mass turns that curve into a straight line.

How do you make it accurate and safe?

Light gates beat a stopwatch here, because a run lasts only a second or two and your reaction time would be a big part of it. Check the card passes cleanly through both beams, and that the trolley reaches the second gate before the masses hit the floor. After that, nothing is pulling it. Release from the same line every time, without a push. Some labs tilt the runway very slightly, just enough that the trolley keeps rolling at a steady speed after a gentle nudge, which cancels out friction.

On safety: put a cushion or a box under the hanging masses and keep your feet clear of them. Put a stop at the end of the runway, or have someone ready to catch the trolley, so it cannot run off the bench.

What do exam questions ask about it?

Common questions ask why masses are moved from the trolley to the hanger, and why light gates are better than a stopwatch. Graph questions ask what the shape says about the relationship. You might also work out an acceleration from light gate readings, or a force or mass from F = m a.

Here is one we wrote in the exam style: "Explain why the student moves masses from the trolley onto the hanger, rather than adding new masses, when she increases the force. (2 marks)" The key idea is keeping the total mass that accelerates the same, so the force is the only thing that changes.

Common mistakes

• Taking masses off the hanger and putting them on the bench. That changes the total mass as well as the force.
• Using grams in F = m a. Convert to kilograms first: 100 g is 0.100 kg.
• Forgetting that the hanging masses accelerate too. They are part of the mass in F = m a.
• Using the hanging mass as the force. The force is its weight, m × g, in newtons.
• Letting the masses hit the floor before the trolley reaches the second light gate. After that nothing pulls the trolley, so place both gates where it passes them while the masses are still falling.