# Teaching Laboratories

### Objective

This investigation concerns instantaneous speed, one of the fundamental concepts of kinematics. We will examine a one-dimensional system in which a moving object (a cart) is constrained to move along a straight line (a track). The purpose is two-fold:

1. To gain understanding of the distinction between the vector quantity (velocity) and the scalar quantity (speed).
2. To discover the method of graphical extrapolation to establish the value of an experimental quantity that cannot be measured directly.

### Equipment

The apparatus consists of a cart on wheels with low-friction ball bearings. The cart is constrained to move along grooves in an aluminum track that can be raised to various angles. Along the track there are two photogates that detect the cart when it passes by. A meter stick and a digital balance are also included.

### Objective

This experiment is a basic exploration of friction, both static and kinetic, between an object and a flat surface. The primary goals are:

1. To investigate how the friction force depends on various properties of the surfaces, such as their smoothness, area, and inclination, and on the sliding object’s weight.
2. To understand the difference between static friction and kinetic friction, and the distinction between the associated coefficients of friction.

### Equipment

The equipment for this experiment consists of a PASCO “Discover Friction” set, which includes four trays with three different surfaces on the underside: cork, felt, and plastic. A second identical plastic tray will allow you to explore the effect of varying the surface area. Also included are a PASCO track, an assortment of bar masses, a force sensor, a cookie pan, and talcum powder.

### Objective

There are three objectives for this experiment.

1. To study Newton's Second Law in rotational form.
2. To elucidate the analogies between quantities in translational motion and quantities in rotational motion
( 𝑚 → I , 𝑥 → 𝜃, 𝐹 → 𝜏 ) and to use these analogies to develop expressions for angular quantities such as rotational kinetic energy.
3. To illustrate the dependence of the moment of inertia on the shape of the object as well as on the choice of the axis of rotation.

### Equipment

The equipment for this experiment consists of a PASCO rotational base and several different shapes that can be attached to it (a disk, a ring, an aluminum platform, and a pair of block masses). The masses (and associated errors) of these shapes are given below. A mass set and pulley provide the torque, and a photogate connected to the DataStudio interface records the motion of the system. A ruler and calipers are also available to measure the appropriate dimensions of the system.

### Objective

You will be asked to construct several simple circuits, use an ammeter and a voltmeter to measure current through and voltage across various circuit elements, and compare your results with theoretical predictions. There are three principle objectives:

1. To learn how to construct and analyze, both theoretically and experimentally, simple circuits involving resistors and light bulbs.
2. To gain an understanding of the basic properties of ammeters and voltmeters, and learn how to connect them in existing circuits and how to use them.
3. To experimentally verify Kirchhoff's Rules and discover their usefulness for predicting the behavior of electrical circuits.

### Equipment

The equipment for this experiment includes a regulated power supply, two handheld multimeters, marked “Ammeter” and “Voltmeter,” to be used accordingly, seven wires of various lengths and colors, and a circuit board consisting of two resistors and a lamp.

### Objective

In this experiment, you will directly observe and measure the force with which two current-carrying parallel wires act on one another. The purpose is three-tiered:

1. To experimentally verify that two antiparallel currents repel.
2. To gain an appreciation of the magnitude of this force as a function of current and separation, especially compared to the gravitational force acting on the same wires.
3. To test experimentally Ampère’s law.

### Equipment

A PASCO advanced current balance with a torsion wire and an angular dial scale is the principal apparatus. The instrument is equipped with a counterbalance beam, a damping vane and a parallax-free position indicator. The current balance is an extremely delicate and precise instrument.

Ancillary equipment includes a set of small masses, a compass, a high current power supply (0-18V, 0-20A), and a ruler.

### Objective

The apparatus of this experiment is versatile and is suitable for a comprehensive investigation of the motion of a magnetic dipole in a magnetic field. In particular, the instrument can be used to demonstrate the physical principles behind Nuclear Magnetic Resonance (NMR), one of the important diagnostic tools of modern medicine. Our goals in this introductory experiment are more modest. We will aim to:

1. Elucidate the nature of the magnetic torque.
2. Investigate some of the possible motions of a particle subject only to magnetic and gravitational torques (under nearly frictionless conditions).
3. Verify quantitatively the theoretical prediction concerning the magnitude of the magnetic torque in a static as well as dynamic case, and observe the precession of a magnetic top.

### Equipment

The principle device to be used is the magnetic torque apparatus, M1-A by TeachSpin. It consists of a pair of Helmholtz coils with a brass air bearing in the center, a cue ball with an implanted magnetic disk and a handle, a power supply with various switches and meters, an aluminum rod with a steel tip, and a sliding mass. The Helmholtz coils will provide the external magnetic field. The air bearing allows the cue ball to rotate in a nearly frictionless manner. A digital balance, a ruler, a pair of calipers, and a stopwatch will also be provided.

### Introduction

All oscillatory systems near equilibrium position behave like SHO, that is their motion is arbitrarily close to harmonic oscillations for sufficiently small amplitudes (deflections). Thus SHO behavior can be studied in many systems in addition to the “classic” spring-and-mass arrangement (which is the subject of W1). From the experimental point of view, and because of its numerous applications, torsional “pendulum” is a particularly convenient SHO device. In the simplest version, which will be employed here, it consists of a wire or fiber (under some tension) suspended from above and possibly also from below, with a symmetric mass (called a rotor) attached to it.

### Equipment

The complete Torsional Oscillator apparatus from TeachSpin. The device consists of a rotor suspended by a vertical steel string under tension, which can twist. The system allows for three kinds of damping: constant (using mechanical friction), proportional to angular speed (using eddy currents), and proportional to angular speed square (using air-drag) – the second of these will be used in the main part of this experiment. External forcing can be provided using a pair of Helmholtz Coils, and a permanent (neodymium) magnet attached to the string.

### Introduction

Every object radiates electromagnetic waves due to the vibration of atoms near its surface (these vibrations, and the radiation, would cease only at absolute zero). Solids and liquids emit radiation in a certain range of frequencies dependent on the temperature and the character of the emitting surface. They also absorb radiation in the same range of frequencies. A blackbody is an object that completely absorbs electromagnetic radiation at all frequencies. Such an object will also be a perfect emitter.

### Equipment

PASCO Thermal Radiation System, including a Leslie Cube, high temperature radiation source (Stefan-Boltzmann lamp) and radiation sensor. Note that the sensor measures power but for a given emitter its reading is proportional to the intensity. Also provided are a low-voltage power supply (20 V, 5 A) and a digital multi-meter.