6.1 – Investigating Accelerated Motion Using a Trolley or Rider (Leaving Cert Physics): Revision Notes

6.1 – Investigating Accelerated Motion Using a Trolley or Rider

This experiment investigates how objects accelerate when moving under the influence of gravity. There are two main experimental methods you can use to measure and analyse accelerated motion in the laboratory.

Overview

Both experimental methods involve creating controlled accelerated motion and then measuring the key variables - initial velocity (u), final velocity (v), acceleration (a), and time (t). By collecting this data, we can verify the equations of motion and understand how objects behave when they accelerate uniformly.

Method A: Trolley with ticker timer

This method uses a trolley moving down an inclined runway, with a ticker timer creating a record of the motion on ticker tape.

Equipment needed

• A trolley and runway
• Ticker timer and ticker tape
• Suitable AC power supply
• Metre stick
• Thumbtack or sticky tape

Experimental procedure

Setup phase:

1. Clean the runway and trolley wheels thoroughly to remove any dirt or grit that might affect the motion

2. Raise one end of the runway and place it on blocks or books, creating a gentle slope so the trolley will accelerate when released

3. Position the ticker timer at the high end of the runway and thread the tape through it, then attach the tape to the trolley

Data collection phase:

4. Switch on the timer and release the trolley to let it accelerate down the runway

5. Stop the trolley at the end of the runway, switch off the timer, and remove the tape

Analysis phase:

6. Examine the ticker tape - ignore the first few blurred dots and measure the length of two adjacent spaces near the start ($s_1$) and two adjacent spaces near the end ($s_2$)

7. Count the number of spaces ($n$) between the middle dots of these measured sections

8. Record your measurements in a data table and calculate the motion variables using the formulas provided

Key formulas for Method A

• Initial velocity: $u = \frac{s_1}{n/50}$
• Final velocity: $v = \frac{s_2}{n/50}$
• Time: $t = n \times \frac{1}{50}$
• Acceleration: $a = \frac{v-u}{t}$

Improving accuracy

Repeat the experiment with the runway at different slopes to obtain different acceleration values and verify your results.

Method B: Air track with timing gates

This method uses a rider moving along an air track, with timing gates measuring how long it takes for a card to pass through light beams.

Equipment needed

• Linear air track with air blower
• Rider with attached card
• Scalar timer
• Two timing gates
• Retort stands (depending on timing gate type)
• Metre stick, scale pan, pulley, thread, and weights

Experimental procedure

Setup phase:

1. Set up the air track on a bench and adjust the levelling screws until it appears reasonably level

2. Connect the air blower and place the rider on the track, then fine-tune the levelling until the rider moves smoothly without drifting

3. Mount each timing gate on a retort stand and connect them to the scalar timer

4. Check the timer operation - the display should change when you interrupt each light beam

Creating acceleration:

5. Connect the rider to weights via a thread over a pulley at one end of the track

6. Position one timing gate near each end of the track, ensuring the card on the rider will interrupt both light beams

Data collection:

7. Release the rider and let it accelerate along the track

8. Catch the rider at the end and switch off the air blower

9. Record the transit times ($t_1$ and $t_2$) and measure the distance between gates ($s$) with a metre stick

10. If the card length ($l$) is unknown, measure and record this value too

Key formulas for Method B

• Initial velocity: $u = \frac{l}{t_1}$
• Final velocity: $v = \frac{l}{t_2}$
• Acceleration: $a = \frac{v^2 - u^2}{2s}$

Improving accuracy

Repeat the experiment with different weights on the scale pan to achieve different acceleration values.

Sources of experimental error

Understanding and minimising error sources is essential for obtaining reliable experimental data in both methods.

Method A (Ticker timer)

• Friction: Dirt or grit on the runway or wheel surfaces can cause velocity variations - keep equipment clean
• Wheel rotation: If trolley wheels cannot rotate freely, this affects motion - lubricate wheel bearings if necessary
• Measurement errors: Use the metre stick correctly to avoid parallax error when measuring distances

Method B (Timing gates)

• Parallax error: Ensure you measure the card length accurately with the metre stick
• Card alignment: The card must be parallel to the direction of motion for accurate timing
• Light beam alignment: The light beam must be perpendicular to both the card and the direction of motion

Analytical questions

Understanding the principles behind these experiments helps you interpret results correctly and identify when measurements are accurate.

1. Recognising acceleration: You can tell the trolley was accelerating because the spaces between dots on the ticker tape get progressively larger

2. Formula application: When using $a = \frac{v^2 - u^2}{2s}$, measurements must start from the first dot produced on the tape to ensure accuracy - starting from a later dot introduces systematic error

3. Experimental precautions: Key steps for accurate results include ensuring clean surfaces, proper alignment, and careful measurement techniques