Question

In an experiment where you are calculating the velocity of the shuttle using an airtrack what would be some random and systematic errors that may occur ? How would each error propagtes to affect the velocity of the shuttle or the balance of kinetic and potential energy in each trail

Answer 1

Solution :

The experiment to calculate velocity of the shuttle using an airtrack is based on the principle of Newton's second law of Motion. It states that, " A change in the motion is proportional to the the external force applied, and occurs in the direction in which the external force is applied."

This gives the equation F=ma, where m= mass of the object (measured in kg) and a= acceleration (measured in m/s²) of the object due to the applied force, F ( measured in N).

This experiment is an attempt to verify Newton's second law of motion- theoretically and experimentally.
By theory, a known force F is applied, accelerating an object that is assumed to be frictionless. And, the values of acceleration are compared with an actually obtained acceleration values with that of theoretically calculated ones.
By experiment, Acceleration is calculated using the formula,

where, = experimentally obtained velocity (in m/s)
= time measured (in s)

Here, random errors and systematic errors creep in.

Random errors : They are errors or fluctuations that occur during the process of taking measurement in the experiment. They always occur in a process of experiment, and can only be minimized by taking average values.

The following random errors might occur during the experiment-

1) is a sensitive measurement. That is because, the measurement of time in this experiment takes place in three different places. They are:

• t₁= time taken by the shuttle to pass through the first photogate.
• t₂= time taken by the shuttle to pas through the second photogate.
• t₃= time between t₁ and t_2.

2) There is a good possibility of unaccounted disturbances, like vibrations during this experiment.

3) Human error in measuring/reading distances and velocity or also occur during the experiment.

Systematic Errors refers to a consistently occurring error in correspondence with the true value. These errors are predictable and can be reduced to an extent, thereby improving the accuracy of the experimental results.

The following systematic errors might occur during the course of the experiment-

1) If the instrument used for measurements are not calibrated accordingly, the error might reflect in the values of the experiment.

2) Measurement using faulty instruments/scales will lead to systematic errors.

Since, we consider a frictionless system, the mechanical energy of the system tends to be constant. Also, since we have considered average values for the measurement, random errors are minimized to an extent. It is important to note that, the Error% is statistically infinitesimally small to make a significant difference in the velocity of the shuttle or the balance of Kinetic Energy and Potential Energy in each trail.