5.1 – Investigating Constant Velocity Using a Trolley or Rider (Leaving Cert Physics): Revision Notes

5.1 – Investigating Constant Velocity Using a Trolley or Rider

This experiment explores the concept of constant velocity through two different methods. Constant velocity occurs when an object moves in a straight line at a steady speed, meaning both the magnitude and direction of motion remain unchanged. Understanding how to measure and verify constant velocity is fundamental to kinematics and forms the basis for more complex motion studies.

What is constant velocity?

Constant velocity means an object travels equal distances in equal time intervals along a straight path. Unlike speed, which is scalar, velocity is a vector quantity that includes both magnitude and direction. When we investigate constant velocity in the laboratory, we're looking to confirm that an object maintains the same velocity throughout its motion.

Method A: Trolley and ticker timer investigation

Purpose and principle

This method uses a trolley moving along a runway while attached to ticker tape that passes through a ticker timer. The timer creates evenly-spaced dots on the tape at regular intervals (every 1/50th of a second), providing a permanent record of the trolley's motion that can be analysed to determine velocity.

Equipment required

The essential apparatus includes a trolley with low-friction wheels, a suitable runway or track, a ticker timer operating at 50 Hz, ticker tape, a power supply for the timer, a metre stick for measurements, and a thumbtack to secure the tape to the trolley. Additionally, wooden blocks or books are needed to raise one end of the runway slightly to compensate for friction.

Experimental procedure

Setting up the apparatus requires careful attention to ensure accurate results. First, clean the runway and trolley wheels thoroughly to remove any dirt or grit that could affect the motion. The runway must be slightly inclined by raising one end using wooden blocks, creating just enough slope for the trolley to overcome friction and move at constant velocity when given a gentle push.

The ticker timer should be positioned at the raised end of the runway with ticker tape threaded through it and attached to the trolley using a thumbtack. Ensure the tape moves freely through the timer without binding. When the timer is switched on and the trolley given a gentle push, it should travel down the runway at steady speed, creating equally-spaced dots on the tape.

After stopping the trolley and removing the tape, examine the dot spacing. For constant velocity, the dots should be evenly spaced throughout the motion. Measure the distance between several sets of dots (for example, between dots A and B) and count the number of spaces to calculate the time taken using the formula:

$t = \frac{n}{50}$

where $n$ is the number of spaces and the timer operates at 50 Hz.

Data collection and calculations

Velocity calculations use the fundamental equation:

$v = \frac{s}{t}$

where $s$ is the distance travelled and $t$ is the time taken. By measuring different sections of the tape and calculating velocities, you can verify whether the motion was truly at constant velocity. All calculated velocities should be approximately equal within experimental error.

Sources of error in Method A

Several factors can affect the accuracy of this method. Dirt or grit on the runway surface or trolley wheels can cause irregular motion, so thorough cleaning is essential. Friction in the trolley wheels that cannot rotate freely will cause velocity variations - lubricating the bearings helps minimise this problem. Parallax error when using the metre stick for measurements can be avoided by ensuring your eye is directly above the measurement point.

Method B: Air track and light gate investigation

Purpose and principle

This method provides greater precision by using a rider moving along a frictionless linear air track. A light gate connected to a scalar timer measures the exact time taken for the rider to pass through the gate, eliminating many sources of error present in the ticker tape method.

Equipment required

The apparatus consists of a linear air track with air blower, a rider designed to move along the track, a scalar timer for precise time measurement, a light gate that can detect the rider's passage, a retort stand and clamp for positioning the light gate, and a metre stick to measure the length of the card attached to the rider. A spirit level ensures proper track alignment.

Experimental procedure

Begin by setting up the air track on a bench and using levelling screws and a spirit level to ensure the track is perfectly horizontal. Any slope will cause the rider to accelerate or decelerate rather than maintain constant velocity. Connect the air blower to create a cushion of air that allows frictionless motion.

Position the light gate at an appropriate point along the track, ensuring it's perpendicular to the direction of motion. The timing gate should be connected to the scalar timer, which measures transit time accurately. Attach a card of known length to the rider - this card will interrupt the light beam as it passes through the gate.

Reset the timer to zero before each measurement. Give the rider a gentle push so it moves at constant velocity along the track. As the card passes through the light gate, the timer records the transit time automatically. Measure the card length precisely using the metre stick, avoiding parallax error by keeping your eye level with the measurement.

Data collection and calculations

Calculate velocity using:

$v = \frac{l}{t}$

where $l$ is the length of the card and $t$ is the transit time measured by the scalar timer. To verify constant velocity, repeat measurements at different positions along the track or with different initial pushes. Consistent velocity readings confirm uniform motion.

Sources of error in Method B

Despite greater precision, some errors remain possible. Parallax error when measuring card length can be minimised by careful alignment. The card may not be perfectly parallel to its direction of motion, affecting the measurement. The light beam might not be exactly perpendicular to both the card and the rider's direction of travel, introducing systematic error.

Analysis and evaluation

Both methods allow investigation of constant velocity, but each has distinct advantages. The ticker tape method provides a visual record of motion that can be analysed in detail after the experiment, making it easier to identify any variations in velocity. However, it's subject to more sources of error and provides lower precision.

The air track method offers much greater precision and eliminates friction almost entirely, giving more accurate velocity measurements. The digital timer provides precise time measurements, but you only get single velocity readings rather than a continuous record of motion.

When analysing results, look for consistency in calculated velocities as evidence of constant velocity motion. Small variations are expected due to experimental uncertainty, but large variations suggest the motion was not truly uniform.