Required practical 7 — Investigating acceleration

Test Newton's second law $F = ma$ by varying force on a constant-mass trolley, or varying mass with a constant force. Plot graphs to confirm linear relationships.

Apparatus

• Dynamics trolley.
• Bench (preferably tilted slightly to compensate for friction, or on a smooth track).
• String over a pulley.
• Hanging masses.
• Light gates connected to a data-logger (or ticker timer / motion sensor).

Method — Investigation 1: F vs a

1. Set up trolley with light gates spaced at fixed distance apart.
2. Total mass on the system (trolley + hanger + masses) kept constant by transferring masses between trolley and hanger.
3. Hang one slotted mass; release trolley. Record acceleration from light gates.
4. Move masses one at a time from trolley to hanger (increasing accelerating force).
5. Plot $a$ (y-axis) vs $F$ (x-axis). Should be a straight line through the origin: $a \propto F$ for constant mass.

Method — Investigation 2: m vs a

1. Same setup but keep the hanging mass (and so $F$) constant.
2. Add masses to the trolley to change total $m$.
3. Record $a$ for each total mass.
4. Plot $a$ vs $1/m$. Should be a straight line: $a \propto 1/m$ for constant force.

Why transfer masses?

When measuring $a$ vs $F$, total mass of the system (trolley + hanger) must remain constant. If you simply add masses to the hanger, you'd also be adding mass to the system. By transferring them, you increase $F$ without changing total $m$.

Sources of error

• Friction — slows the trolley; offset by tilting the bench until trolley moves at constant v with no force, OR by including friction force in calculations.
• Light gate placement — must be perpendicular to motion, accurately measured separation.
• Air resistance — small at low speeds.
• Pulley friction — assumed negligible.