3.5.2 – Ticker Tape Timer | Physics with Mr Shone

The ticker tape timer is a piece of laboratory apparatus used for analysing the motion of an object.

A ticker tape timer marks dots on a ticker tape at a constant frequency ƒ to measure the speed of a moving object, e.g. 50 dots per second means ƒ = 50 Hz.

A narrow strip of paper is slotted through the ticker tape timer, and attached to a moving object e.g. a trolley T.

As the object moves, it pulls the paper through the ticker tape timer. The distance between the dots will help us measure the speed of the object.

The time interval or duration between two dots (or 1 dot interval or 1 spacing) is given by 1/ ƒ, e.g. if ƒ = 50 Hz, duration of 1 dot interval = 1/ ƒ = 1s / 50 = 0.02 s.

The diagram below shows the pattern on the tape after T has moved a certain distance.

Determining an average velocity:

Time interval between 2 dots (i.e. for each spacing) = 1/ƒ
t is the duration between the points A and B, t=N x 1/ƒ
average velocity, <v> = d/t = d / (N x 1/ƒ)

Example 1
The diagram below shows the pattern on a ticker tape after a trolley T has moved a certain distance. The ticker tape timer makes 60 dots in 1 second. (a) Determine the average velocity in the section PQ. average speed u = d₁ / t₁ = 0.05 m / (3 x 1/60) s = 1.0 m s^-1 (b) Determine the average velocity in the section RS. average speed u = d₂ / t₂ = 0.30 m / (3 x 1/60) s = 6.0 m s^-1 *(c) Hence, state whether the speed of the trolley is increasing, decreasing* or remaining constant. v is higher than u hence the speed is increasing**

Example 1

The diagram below shows the pattern on a ticker tape after a trolley T has moved a certain distance. The ticker tape timer makes 60 dots in 1 second.

(a) Determine the average velocity in the section PQ.

average speed u = d₁ / t₁ = 0.05 m / (3 x 1/60) s = 1.0 m s^-1

(b) Determine the average velocity in the section RS.

average speed u = d₂ / t₂ = 0.30 m / (3 x 1/60) s = 6.0 m s^-1

(c) Hence, state whether the speed of the trolley is increasing, decreasing or remaining constant.

v is higher than u hence the speed is increasing

Advanced Physics: Example 1 Extension
(d) Calculate the average acceleration of the trolley as it moves between P and S. As determined in (a) the average velocity in section PQ is 1.0 m s^-1. It is important to understand this is not the velocity at P nor the velocity at Q, but is the velocity at a midpoint (in terms of time / dots) between these two points. This point is marked A on the above diagram. Similarly, as determined in (b) the average velocity in section RS is 6.0 m s^-1. Which, again, is not the velocity at R nor the velocity at S, but is the velocity at a midpoint between these two points, which here is labelled as B. A and B are separated by 6 spaces. i.e. a time of (6 x 1/60) s = 0.10 s average acceleration, <a> = (v-u)/t = (6.0 – 1.0)/0.10 = 50 m s^-2

Advanced Physics: Example 1 Extension

(d) Calculate the average acceleration of the trolley as it moves between P and S.

As determined in (a) the average velocity in section PQ is 1.0 m s^-1. It is important to understand this is not the velocity at P nor the velocity at Q, but is the velocity at a midpoint (in terms of time / dots) between these two points. This point is marked A on the above diagram.

Similarly, as determined in (b) the average velocity in section RS is 6.0 m s^-1. Which, again, is not the velocity at R nor the velocity at S, but is the velocity at a midpoint between these two points, which here is labelled as B.

A and B are separated by 6 spaces. i.e. a time of (6 x 1/60) s = 0.10 s

average acceleration, <a> = (v-u)/t = (6.0 – 1.0)/0.10 = 50 m s^-2

Example 2
A ticker-tape timer is used to investigate the movement of a trolley. The frequency of the timer is 50 Hz and a portion of the tape is shown below. *Determine if the trolley was speeding up, slowing down* or moving with constant speed.**

Example 2

A ticker-tape timer is used to investigate the movement of a trolley. The frequency of the timer is 50 Hz and a portion of the tape is shown below.

Determine if the trolley was speeding up, slowing down or moving with constant speed.

Links
https://www.physicsclassroom.com/Concept-Builders/Kinematics/Name-That-Motion/Concept-Builder

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