Required Practical 19: Investigating Force, Mass and Acceleration

Mark equally spaced lines across the bench, for example every 0.20 m over a distance of 1.0 m. Attach the pulley securely at the far end. Tie the string to the car, pass it over the pulley and attach the hanger to its other end. Keep the string horizontal and aligned with the car.

The weight of the hanging masses provides the driving force. As the hanger falls, the car moves towards the pulley. Both accelerate, so the relevant moving mass includes the car, the hanger and all added masses. Friction opposes the motion; the resultant force on this moving system is therefore less than the hanging weight.

Choose a hanging weight that gently accelerates the car, leaving enough time to record its motion. Ensure the hanger can descend freely without reaching the floor during the measurements. Keep feet clear of falling masses, secure the pulley and stop the car before it reaches the bench edge.

Measuring acceleration rather than just journey time

Release the car from the same starting position without pushing it. Start the stopwatch on release and record the elapsed time at each marked line, using lap timing. Repeat each condition several times and calculate mean elapsed times for the lines.

Subtract successive elapsed times to find the time spent in each distance interval. Calculate the average speed over each interval:

$\text{average speed} = \frac{\text{interval distance}}{\text{interval time}}$

For example, if equal distances take progressively shorter times, the car’s speed is increasing. One average speed for the entire journey would hide this change.

Because the car travels in one direction, these speeds can be used to estimate its change in velocity. Treat each interval’s average speed as an estimate of its speed at the midpoint in time of that interval. Compare an early and a later interval, then calculate:

$a = \frac{v-u}{\Delta t}$

Here, $u$ and $v$ are the earlier and later estimated speeds, and $\Delta t$ is the time between their interval midpoints. This gives an estimate of acceleration from the motion measurements.

Changing force while keeping mass constant

The independent variable is the driving force; the dependent variable is acceleration. Keep the total moving mass constant.

Begin with masses on the hanger, then reduce the hanging weight in steps. A small weight stack could provide 1.0 N, reduced in steps of 0.2 N. Every mass removed from the hanger must be transferred to the car and secured. This changes the driving force without changing how much total mass must accelerate.

For each force, repeat the release and timing procedure and calculate acceleration. Keep the bench surface, starting position, distance intervals and release method unchanged.

Plot acceleration on the vertical axis against driving force on the horizontal axis. Acceleration should increase as force increases. Ideally, acceleration is directly proportional to the resultant force at constant mass. Friction can make a graph against hanging weight depart from a straight line through the origin.

Changing mass while keeping force constant

Now keep the hanging mass unchanged and add different masses to the car. The independent variable is total moving mass; acceleration is again the dependent variable. Include the hanger and its masses when calculating each total.

Repeat the same motion measurements for each mass. Keeping the hanging weight unchanged keeps the driving force constant; use the same bench and apparatus to keep friction as similar as possible.

Acceleration should decrease as total mass increases. Ideally, at constant resultant force, doubling the mass halves the acceleration: $a \propto 1/m$. An acceleration–mass graph is therefore a decreasing curve, not a straight descending line.

Judging the quality of the measurements

Short travel times make stopwatch reaction time a substantial source of error. Gentle acceleration makes timing easier, while repeating measurements and taking means reduces the effect of random variation.

Videoing the car and marked lines allows crossing times to be read from the recording, reducing reliance on human reaction time. Friction remains a limitation: repeats do not remove a persistent opposing force. Interpret the results as a test of the predicted trends while recognising that hanging weight is not necessarily equal to resultant force.

Use the time between the midpoints of the intervals used to estimate $u$ and $v$.

Two investigations

Total moving mass includes the car, hanger and added masses.

Results and evaluation

• At constant mass: greater resultant force gives greater acceleration.
• At constant resultant force: greater mass gives smaller acceleration.
• Friction means resultant force is less than hanging weight.
• Video improves timing; repeats and means reduce random variation.
• Secure apparatus and keep clear of falling masses.