1.10 - Investigating Motion

Force, mass and acceleration - Apparatus and method

• This experiment investigates how the acceleration of an object depends on the force applied to it and on its mass.
• It uses the relationship force = mass × acceleration.

Apparatus

• A trolley on a flat bench or runway, carrying a piece of card that interrupts a light gate
• A light gate connected to a data logger
• A string running over a pulley fixed at the edge of the bench
• A hanging hook holding slotted masses, attached to the other end of the string
• A balance to measure the masses

The card has a gap in the middle, so it interrupts the beam twice as it passes. The light gate measures the trolley's speed at two moments a fraction of a second apart, and the data logger uses these to calculate its acceleration.

Method

1. Measure the mass of the trolley, the slotted masses and the hook. Enter the length of the card sections into the data logger.
2. Connect the trolley by string over the pulley to the hook. The weight of the hook and masses provides the accelerating force for the whole system (trolley, hook and masses combined).
3. Mark a starting line so the trolley always travels the same distance to the light gate.
4. Place the trolley on the starting line with the string taut, then release it.
5. Record the acceleration measured as the trolley passes through the light gate.
6. Repeat twice more and calculate an average acceleration.

Reducing friction

Friction between the trolley and the bench affects the measurements. Two common ways to reduce its effect:

1. Air track - Floats the trolley (or glider) on jets of air so there's almost no friction.
2. Tilted runway - Tilt the runway slightly until the trolley moves at a steady speed when given a gentle push. This compensates for friction, so the hanging weight is the only force accelerating the trolley.

Varying the mass and varying the force

Using the same apparatus, change one variable at a time while keeping the other constant.

Changing the mass (force kept constant)

• Add masses to the trolley one at a time to increase the mass of the whole system.
• Do not add masses to the hook, as that would change the accelerating force.
• Record the average acceleration for each total mass.

Acceleration decreases as mass increases - mass and acceleration are inversely proportional.

Changing the force (mass kept constant)

1. Start with all the slotted masses loaded on the trolley.
2. Transfer masses to the hook one at a time to increase the accelerating force.
3. Record the average acceleration for each force.

Masses are transferred rather than added so the total mass of the system stays constant. Acceleration increases as force increases - force and acceleration are directly proportional.

Plotting the results

• Acceleration against force - A straight line through the origin, showing acceleration is directly proportional to force.
• Acceleration against mass - A curve showing an inverse relationship.
• Acceleration against 1 ÷ mass - A straight line through the origin, confirming acceleration is inversely proportional to mass.

Choosing equipment to measure distance and time

Speed is calculated from a measured distance and time:

$$\text{Speed}=\frac{\text{distance}}{\text{time}}$$

Measuring distance

• Use an instrument longer than the distance being measured to avoid moving it along.
• Under a metre (lab experiments) - A ruler or metre stick.
• Larger distances (e.g. walking speed over several metres) - A tape measure or trundle wheel.

Measuring time

• Longer intervals (more than about 5 seconds) - A stopwatch is suitable.
• Very short intervals (e.g. a trolley passing a point) - Light gates connected to a data logger are best.
• A stopwatch involves human reaction time, which introduces a significant percentage error into short time measurements.

Video analysis as an alternative

1. Record the motion on video alongside a metre ruler and view it frame by frame.
2. Count how many frames the object takes to travel a set distance on the ruler:

$$\text{Time taken}=\frac{\text{number of frames}}{\text{frame rate (fps)}}$$

Speed is then calculated from distance ÷ time.

Distance, speed and acceleration on a ramp and runway

Apparatus and method

• A vehicle is released from a marked starting line near the top of a ramp that leads onto a flat runway.
• Light gates connected to a data logger record the time the vehicle passes each point using an attached card.
• Release the vehicle from the start line so it rolls down the slope and along the runway.
• Repeat several times and calculate average times.

As the vehicle rolls down the ramp it accelerates; on the runway it moves at a roughly constant speed (ignoring friction).

Finding the speeds and acceleration

• Average speed on the ramp = distance between the ramp light gates ÷ time taken between them. Runway speed is found the same way using the runway gates.
• Acceleration down the ramp = (final speed - initial speed) ÷ time taken. The initial speed at release is zero, and the final speed is the speed at the bottom of the ramp.
• Instantaneous speed at a single gate = width of the interrupting card ÷ time the beam is blocked. A double-interrupt card gives two instantaneous speeds a known time apart, allowing the data logger to calculate acceleration directly.

Factors to investigate

Change one factor at a time to investigate what affects the motion:

• The mass of the vehicle, by adding weights to it
• The friction, by placing different surface materials on the ramp
• The release height, by starting the vehicle higher up the ramp
• The angle of the ramp

A steeper ramp or less friction increases acceleration down the slope. Releasing the vehicle from higher up increases its speed at the bottom of the ramp.