Section 1 of 7The idea behind the investigation
Newton's second law
- Newton's second law The acceleration of an object is directly proportional to the resultant force on it and inversely proportional to its mass.
- As an equationF = m × a, with force in newtons (N), mass in kilograms (kg) and acceleration in metres per second squared (m/s2).
Two separate experiments
- Two separate experiments Experiment 1 changes the force while the mass of the whole system is kept constant.
- Experiment 2 changes the mass while the force is kept constant.
Equipment
- Equipment Trolley, runway or bench, pulley, string, slotted masses on a hanger, metre ruler, stopwatch or light gates, and a balance.
- Typical resolutionruler 1 mm, stopwatch 0.01 s.
Section 2 of 7Method for Experiment 1: varying force
1
Mark a start line and a finish line a known distance apart (for example 1.0 m) on the bench using the metre ruler.
2
Fix a pulley to the edge of the bench. Tie string to the trolley, pass it over the pulley and attach a mass hanger to the other end. Keep the string horizontal.
3
Put all the slotted masses you will use on the trolley at the start, so the total mass of the moving system never changes.
4
Move one 0.1 N mass at a time from the trolley to the hanger. The pulling force is the weight on the hanger, W = m × g.
5
Hold the trolley at the start line, release it and start the stopwatch together. Stop the clock as the front of the trolley crosses the finish line.
6
Repeat each force at least three times and calculate the mean time. Then increase the force by moving another mass to the hanger and repeat.
Section 3 of 7Variables in the two experiments
| Experiment | Independent variable | Dependent variable | Control variables |
|---|---|---|---|
| 1: force and acceleration | Resultant force (weight on the hanger) | Acceleration of the trolley | Total mass of trolley, masses and hanger; the distance; the surface |
| 2: mass and acceleration | Mass of the trolley (add masses to it) | Acceleration of the trolley | Force pulling it (the same hanger load); the distance; the surface |
Section 4 of 7Processing the results
1Find the mean time
- Find the mean time Average the repeat readings of time t for each setting and ignore any obvious anomaly.
2Calculate acceleration
- Calculate acceleration From rest over distance s, use a = 2s ÷ t2.
- Alternatively find the final speed with light gates and use a = (v − u) ÷ t.
3Plot for force
- Plot for force Plot acceleration against force (Experiment 1).
- A straight line through the origin shows direct proportionality.
4Plot for mass
- Plot for mass Plot acceleration against 1 ÷ mass for Experiment 2.
- A straight line through the origin shows acceleration is inversely proportional to mass.
Section 5 of 7Safety, accuracy and improvements
Safety
- Safety Place a cushion or sand tray to stop the masses and trolley falling on feet.
- Stop the trolley before it reaches the pulley.
Reducing errors
- Reducing errors Light gates and a data logger remove the reaction-time error of a hand-held stopwatch.
- Use a longer track so times are larger and the percentage error from timing is smaller.
Friction
- Friction Friction acts against the motion and lowers the resultant force.
- Tilting the runway slightly can compensate for it.
Section 6 of 7Key terms
| Term | Meaning |
|---|---|
| Resultant force | The single force that has the same effect as all the forces acting on an object. |
| Independent variable | The quantity you deliberately change in an investigation. |
| Dependent variable | The quantity you measure to see the effect of the change. |
| Control variable | A quantity kept the same so that it cannot affect the result. |
| Directly proportional | Two quantities whose graph is a straight line through the origin. |
| Resolution | The smallest change in a quantity that a measuring instrument can show. |
Section 7 of 7Exam technique
1
Adding extra masses to the hanger without taking them from the trolley. This changes the total mass and ruins the control; move masses across instead.
2
Using the whole weight of the trolley as the pulling force. The accelerating force is only the weight of the hanger load.
3
Timing with a stopwatch once and quoting that as the result. Repeat and take a mean.
4
Forgetting that a = 2s ÷ t2 only works when the trolley starts from rest.
5
Saying friction does not matter. It reduces the resultant force and is a source of systematic error.