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## Determining the velocity and acceleration of a body using a ticker Tape Time (Compensation For Friction)

Before each experiment with a trolley, it is necessary to compensate for friction.

This can be done by tilting the runway with suitable packing pieces until it moves with uniform velocity after having been given a slight push.

A paper tape is driven through a ticker timer connected to a mains supply of known frequency e.g 50Hz by a trolley running freely on an inclined plane.

After the trolley has reached the end of the run way, the tape is removed and marked every after 5dots.The first mark made is the zero tme.

**OR**

The procedures are repeated, various velocities determined and a graph of velocity against time plotted. The slope of the graph gives the acceleration of the body.

Using the ticker tape timer to determine Acceleration After it has printed dots on A tape.

Determining the velocity and acceleration of a body using a ticker Tape Time also may involve in,

**Frequency: **These are vibrations per second or number of dots per second. The S I unit is Hertz. (Hz).

**Example:** A frequency of 60Hz mean 60 dots per second.

**NB:** Frequency is also number of dots printed per second.

Period: This is the time taken for a dot to be printed on a tape. The SI unit of period is seconds.

**Example: 1**

Below is a tape printed by ticker- tape timer vibrating at 100Hz. Find the time taken to print these dots.

**Example: 2**

Below is a tape printed by a ticker –tape timer vibrating at 50Hz. Calculate the average speed.

**Calculating the initial velocity “u” and final velocity “v” from the tape.**

**Example:3**

Below is a tape printed by a timer vibrating at 50Hz

Calculate the;

i) Initial velocity

ii) Final velocity

iii) Acceleration

For the above, the following steps should be involved.

identifying the frequency

finding the periodic time from T= 1/f

finding the time taken to cover given distances

calculating the required velocities

finding the time taken to cover distance between mid points of the distances

calculating the required acceleration

**Example II:**

Below is a tape printed by a ticker timer vibrating at 20Hz. Calculate the acceleration.

**Example III**

The timer is vibrating at 20Hz. Calculate the acceleration

**Solution**

If there are n-dots, then there are (n-1) spaces.

i.e∶ 𝒏𝒔=(𝒏𝒅−𝟏).

Where ns is the number of spaces and nd is the number of dots.

**Example:**

A ticker timer is vibrating at 10Hz. Calculate the time taken if the timer prints 21 dots.

**Example:**

A ticker timer prints 11 dots at 20Hz in a space of 2m. Calculate the average speed.

**Note:**

In experiments with ticker timer being pushed by a trolley, the first dots are ignored because they are overcrowded for accurate measurements.

**Calculating Acceleration from given number of dots.**

If the distance is measured from mth dot to nth dot then the number of spaces can be calculated directly by subtracting m from n.

**Example:**

A trolley is pulled from rest with a constant force down an inclined plane. The trolley pulls a tape through a ticker timer vibrating at 50Hz. The following measurements were made from the tap.

Distance between 16th dot and 20th dot= d1=20cm

Distance between 20th dot and 30th dot = 34cm

Distance Q between 30th dots and 40th dot = 48cm

Distance between 40th dot and 50th dot = d2=62cm

Calculate the acceleration of the trolley.

**Solutions**