Newton's second law: accelerating a trolley with hanging masses

The idea

The acceleration of an object is proportional to the net force on it and inversely proportional to its mass, so F = m a can be tested by changing one and measuring the other.

See it in the Concept Studio

• Acceleration is net force divided by massRun it

What you need

• dynamics trolley 1.0 kg with low-friction wheels, 1
• 1.5 m runway or bench with a pulley clamped at the end, 1
• string 1.5 m, 1
• slotted masses 10 g x 10 with hanger, and 500 g bars x 2 to load the trolley
• two light gates with timer, or a motion sensor, or a ticker timer, 1 set
• interrupt card 10.0 cm for the light gates, 1
• metre rule and wooden wedge to tilt the runway, 1 each

How to do it

1. Friction compensation: tilt the runway with the wedge until the trolley, once nudged, rolls at constant speed (equal light-gate times or evenly spaced ticker dots).
2. Tie the string to the trolley, pass it over the pulley and hang the 100 g hanger. Place the light gates 0.50 m apart, and set the release point so the hanger is still clear of the floor when the trolley passes the second gate.
3. Release the trolley from rest before the first gate; record the speed at each gate and the time between them; acceleration = (v2 - v1) / t. Three runs, average.
4. Force series: move mass from the trolley to the hanger in 10 g steps so the total accelerating mass stays 1.10 kg, giving hanging forces of 0.098 N up to 0.98 N. Record the acceleration for each.
5. Mass series: keep 100 g hanging and add 500 g and then 1000 g to the trolley. Record the acceleration for each total mass.
6. Plot acceleration against force (straight line through the origin) and acceleration against 1 / total mass (straight line through the origin); find the gradients.

What you should see

With 100 g hanging (force 0.98 N) and a total moving mass of 1.10 kg the acceleration is 0.89 m/s^2 and from rest the trolley covers 0.50 m in 1.06 s; measured values are lower where friction compensation is imperfect. Doubling the hanging force doubles the acceleration. In the mass series the acceleration falls to 0.61 m/s^2 for 1.60 kg and 0.47 m/s^2 for 2.10 kg, so acceleration x total mass stays 0.98 N. The acceleration against force graph has gradient 1 / (1.10 kg) = 0.91 per kg. The learner knows it worked when both graphs are straight through the origin.

What changes

What you change

hanging force (N) with total mass fixed, then total mass (kg) with force fixed

What you measure

acceleration (m/s^2)

What you keep the same

• friction-compensated runway
• same string and pulley
• release from rest at the same point
• total moving mass constant in the force series

Common misconceptions

Each of these ideas is wrong, and the practical is a chance to test it.

• A constant force produces a constant speed.
• The hanging mass's weight is the only mass being accelerated.
• A stationary trolley with a small hanging mass has a net force on it.

Safety card

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this practical supports. They are references, not a verified or complete curriculum alignment.

• Science 7–10 Syllabus (2023)SC5-WAM-02SC5-WS-04SC5-WS-05SC5-WS-06
• Australian Curriculum v9AC9S10U05AC9S10I02AC9S10I03AC9S10I04AC9S10I05

Sources

The pages the author read to write this practical.

1. curriculum.nsw.edu.au/learning-areas/science/science-7-10-2023/outcomes
2. curriculum.nsw.edu.au/learning-areas/science/science-7-10-2023/content/stage-5/faafd3c3df
3. spark.iop.org/investigating-newtons-second-law-motion
4. spark.iop.org/relationships-between-acceleration-force-and-mass
5. spark.iop.org/trolley-and-falling-mass
6. spark.iop.org/compensating-friction