mechanics

Wilberforce Pendulum

Student Manual

The harmonic oscillator, with all its manifestations, is an extensively studied system. It possesses a single degree of freedom. More complicated systems have more degrees of freedom, for example, two pendulums connected by a spring. In such cases, the behaviour of each variable influences the other which leads to a coupling between the individual degrees of freedom. Energy can toggle between the two degrees of freedom. A well-known example is the Wilberforce pendulum, where the oscillation alternates between the longitudinal stretching of a vertical spring and the rotation of a cylindrical object hung at the end of that spring. The aim of this experiment is to investigate the dynamics of the Wilberforce pendulum.

Software Code Phystrack&nbsp(Download)
Sample Results Vertical oscillations for various moments of inertia
Fourier contents for various moments of inertia
Square of difference of squares of normal modes versus inverse of moments of inertia
Hardware Manual Machining dimensions of the oscillating mass
Experiment Code 2.24
Version Version 2018-1

Further Readings and References


Pictorial Procedure

By Azeem Iqbal | Lab 2 . Smart Physics
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Steering paramagnetic Leidenfrost drops in an inhomogeneous magnetic field

Student Manual

The Leidenfrost Effect is a phenomenon in which a liquid drop levitates on a surface that is significantly hotter than its boiling point. When we create Leidenfrost drops using a paramagnetic liquid, such as oxygen, we end up with liquid drops that hover above a surface with negligible friction, and since oxygen is paramagnetic, can be controlled by a magnetic field.

Software Code Tracker&nbsp(Download)
Experiment Code 2.23
Version August 28, 2018 Version 2018-1

Further Readings and References


Pictorial Procedure

Hardware Description

The copper cone is 10cm in height and 10cm in diameter. It holds enough liquid nitrogen to get a supply of liquid oxygen drops for around a couple of minutes. Underneath the tip of the cone is an aluminium bar with a depression along it’s axis. This is to make sure that the drop moves in a straight line as it enters the horizontal sheet. It allows us to vary the initial displacement of the drop (as explained in the video). This sheet is made of plexiglass, which is a cheap solution, but has some problems. The scratches on the surface of this sheet are very prominent in light, so we use a permanent marker to reduce light reflecting from the scratches. The screws near the corners of the sheet allow us to make sure that the sheet is horizontal. This is to ensure that the only force affecting the motion of the drops is the magnetic force. However, since this is a low cost setup and we only ensure that the sheet is horizontal using a spirit level, gravity does affect drops at very slow velocity. The plexiglass walls around the cone ensure that very little nitrogen vapours enter the recording area and makes sure the video recordings are clear and easy to analyse.

We need to make sure that we make no contact with any cold surface during the experiment. We use gloves for handling the glass that is used to pour liquid nitrogen. The cone must not be touched during the experiment, and even after the nitrogen has evaporated. The aluminium bar is not cold enough to be dangerous, but should still preferably not be touched with bare hands. The copper cone should be stable enough so that it can’t be accidentally tipped over while performing the experiment.

 

By Azeem Iqbal | Lab 2
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Ring on a Rotating Shaft

Student Manual

A “ring oiler” is a simple mechanical device that is traditionally used for lubrication of bearings. In this machine, a shaft is rotated with a motor. A ring is mounted on the shaft and co-rotates with the shaft. As it rotates it also moves sideways along the length of the shaft. The ring is large enough that it dips in a reservoir of oil, bringing oil up to the shaft and lubricating the shaft and the bearings. We will not use oil as our purpose is not to lubricate, rather investigate the strange mechanical motion of the ring as it roto-translates along the shaft.

Hardware Manual Circuit Diagram
Experiment Code 2.22
Version July 24, 2018, Version 2018-1

Further Readings and References

  • A loose-ring lubricator model
    Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science , G. E. Innes, D Dowson and C. M. Taylor , 213 199-209 , (1999).

Pictorial Procedure

By Azeem Iqbal | Lab Two Tasks
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When are two measurements “same” or “different”? Example of conical shaped pendulums

Student Manual

We have designed a simple experiment using conical shaped pendulums, to see where experiment matches theory. It is customary in practical work to ask when two measurements “match” and when do they “differ”. Furthermore we need to find agreement of experiment with theory. This experiment aims to quantify the similarity (or difference) between various measurements.

Experiment Code 1.21
Version 2018-v1

Further Readings and References


Pictorial Procedure

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A Doubly Suspended Pendulum

bifilar_pic_1

Student Manual

The objective of this experiment is to determine the moment of inertia of a bi lar pendulum experimentally and then comparing it to the theoretical prediction. The investigation of the bi lar pendulum includes determining the accuracy of the moment of inertia inferred from the experiment and understanding the underlying experimental process.

Sample Results A graph showing relationship between time period and inverse of D (distance between the two filars)
Experiment Code 1.19
Version May 12, 2017

Further Readings and References


Pictorial Procedure

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Vertical pendulum in phase space

Student Manual

A paradigmatic physical system is the physical pendulum is experimentally studied using the acceleration and rotation. A smart phone sensor is used to analyze a vertical pendulum, which is in fact a bicycle wheel. The sensors used in the experiment include the smartphone’s inbuilt gyroscope and accelerometer. Gyroscope is used to measure angular velocity of the wheel while the accelerometer is used to measure the linear acceleration of wheel. A smartphone is fixed to the outside of a bicycle wheel whose axis is kept horizontal and fixed. The compound system, wheel plus smartphone, defines a physical pendulum which can rotate, giving full turns in one direction, or oscillate about its equilibrium position (performing either small or large oscillations). Measurements of the radial and tangential acceleration and the angular velocity obtained with smartphone sensors allows a deep insight into the dynamics of the system.

Sample Results Phase space of angular velocity and angular acceleration
Plot of angular velocity vs time
Combined plot of radial acceleration with angular velocity
Experiment Code 5.5
Version 2016-v1

Further Readings and References

  • Phase space
    Exploring phase space using smartphone acceleration and rotation sensors simultaneously , Martín Monteiro, Cecilia Cabeza and Arturo C Martí , European Journal of Physics, Volume 35 , (2014).

Pictorial Procedure

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Rotational Motion About a Fixed Axis

Student Manual

This task is similar to the experiment “Sliding Friction” where we used the video motion tracking to investigate the friction between the surfaces of a linearly sliding body and a static surface. In this task, we will investigate friction accompanying rotational motion. A disc will be attached to a shaft and manually rotated. Friction will decelerate the rotating disc. We will record this motion on a high speed camera and investigate some interesting aspects of angular kinematics.

Sample Results Curve Fitting for Displacement
Curve Fitting for Velocity
Experiment Code 5.2A
Version 2017-1

Further Readings and References


Pictorial Procedure

IMG_0319

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Spring Pendulum

Student Manual

Oscillations are a commonly observed physical phenomenon. In this experiment, we will use our video motion analysis technique to investigate the oscillatory motion of a mass-spring system. We will calculate frequency and damping coefficient of the oscillatory motion.

Sample Results Curve Fitting for Vertical Displacement
Curve Fitting for Vertical Velocity
Experiment Code 5.4
Version 2017-1

Further Readings and References

  • Article 13.1-13.4
    Physics for Scientists and Engineers with Modern Physics , Fishbane, Gasiorowicz and Thornton 366-377 , (1993).

Pictorial Procedure

IMG_0293 IMG_1240 IMG_1241 IMG_1242

Video

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