# Distinguishing between velocity and acceleration

##### Demonstration

This experiment allows you to focus on what happens when a constant force is applied to a trolley: its velocity will change but its acceleration will remain constant. Datalogging enables you to avoid the distraction of calculations and instantly display the acceleration.

#### Apparatus and materials

Light gate, interface and computer

Dynamics trolley

Mass, 200 g, pulley and string

Clamp

Ruler

Double segment black card (see diagram)

#### Health & Safety and Technical notes

Take care when masses fall to the floor. Use a box or tray lined with bubble wrap (or similar) under heavy objects being lifted. This will prevent toes or fingers from being in the danger zone.

Pass a piece of string with a mass hanging on one end over a pulley. Attach the other end to the trolley so that, when the mass is released, it causes the trolley to accelerate. Choose a length of string which allows the mass to touch the ground when the trolley is about two thirds along the bench length.

Fit the trolley with a double segment black card. Clamp the light gate at a height to allow both segments of the card to interrupt the light beam when the trolley moves through the gate. Measure the width of each segment with a ruler and enter the values into the data-logging software. Connect the light gate via an interface to a computer programme.

Configure the program to obtain measurements of acceleration derived from the double interruptions of the light beam by the card. The program will require the dimensions of the card. The internal calculation within it involves using the interruption times for the two segments to obtain two velocities. The difference between these divided by the time between them yields the acceleration.

#### Procedure

Data collection

a Pull the trolley back so that the mass is raised to just below the pulley. Position the light gate so that it will detect the motion of the trolley soon after it has started moving. Set the software to record data. Release the trolley. Observe the measurement for the acceleration of the trolley.

b Move the light gate about 20 cm further along the table. Repeat the measurement, releasing the trolley from the same point as before. Observe the new measurement and compare it with the first.

c Repeat this process several times until the light gate is as near as it can be to the pulley, while still allowing the trolley to pass through.

Analysis
Analysis of the data need not be treated formally.

Students should observe that the value of acceleration does not change substantially for successive positions of the light gate. There will however be a point after which the acceleration drops close to zero. This is the point at which the mass reaches the ground, the string becomes slack, and the trolley continues to move due to inertia.

For many students the result comes as a surprise, since they tend to associate the faster moving trolley with a greater acceleration.

#### Teaching notes

1 This is a useful demonstration for provoking thinking about the distinction between velocity and acceleration. The instant presentation of the acceleration, using the software, greatly benefits the discussion by avoiding preoccupation with the calculation process.

2 Through direct observation with the naked eye, the velocity is easily observed to increase, but the rate of change of velocity after the mass touches the ground is much harder to perceive, especially as the trolley by then has achieved its maximum velocity. Skilful leadership of the discussion during the demonstration can sharpen pupils' concept of acceleration as a rate of change of velocity, a concept which is independent of how fast the trolley is actually moving at the time.

3 The demonstration could lead into a discussion of Newton's first two laws of motion. The trolley continues to move at its maximum speed once the string goes slack. This introduces Newton's first law. The trolley only accelerates while the external force is applied to the trolley (via the string). This illustrates Newton's second law.

This experiment was safety-checked in May 2006