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SET UP

Preliminary Set Up
1. Place the support base on a flat, stable table that is located such that the Gravitational Torsion Balance will be at least 5 meters away from a wall or screen. For best results, use a very sturdy table, such as an optics table.
2. Carefully secure the Gravitational Torsion Balance in the base.
3. Remove the front plate by removing the thumbscrews.
4. Fasten the clear plastic plate to the case with the thumbscrews.

Figure 2: Removing a plate from the Chamber Box

Leveling the Gravitational Torsion Balance

1. Release the pendulum from the locking mechanism by unscrewing the locking screws on the case, lowering the locking mechanisms to their lowest positions (Figure 3).

Figure 3: Lowering the Locking Mechanism to Release the Pendulum Bob Arms

2. Adjust the feet of the base until the pendulum is centered in the leveling sight (Figure 4). (The base of the pendulum will appear as a dark circle surrounded by a ring of light).
3. Orient the Gravitational Torsion Balance so the mirror on the pendulum bob faces a screen or wall that is at least 5 meters away.

Figure 4: Using the Leveling Sight Figure 5: Adjusting the Height of the Pendulum

Vertical Adjustment of the Pendulum

The base of the pendulum should be flush with the floor of the pendulum chamber. If it is not, adjust the height of the pendulum:

1. Grasp the torsion ribbon head and loosen the Phillips retaining screw (Figure 5a).
2. Adjust the height of the pendulum by moving the torsion ribbon head up or down so the base of the pendulum is flush with the floor of the pendulum chamber (Figure 5b).
3. Tighten the retaining (Phillips head) screw.

INTRODUCTION

The Gravitational Torsion Balance reprises one of the great experiments in the history of physics—the measurement of the gravitational constant, as performed by Henry Cavendish in 1798.

The Gravitational Torsion Balance consists of two 38.3 gram masses suspended from a highly sensitive torsion ribbon and two1.5 kilogram masses that can be positioned as required. The Gravitational Torsion Balance is oriented so the force of gravity between the small balls and the earth is negated (the pendulum is nearly perfectly aligned vertically and horizontally). The large masses are brought near the smaller masses, and the gravitational force between the large and small masses is measured by observing the twist of the torsion ribbon.

An optical lever, produced by a laser light source and a mirror affixed to the torsion pendulum, is used to accurately measure the small twist of the ribbon.

THEORY

The gravitational attraction of all objects toward the Earth is obvious. The gravitational attraction of every object to every other object, however, is anything but obvious. Despite the lack of direct evidence for any such attraction between everyday objects, Isaac Newton was able to deduce his law of universal gravitation.

Newton’s law of universal gravitation:

where m1 and m2 are the masses of the objects, r is the distance between them, and
G = 6.67 x 10-11 Nm2/kg2

However, in Newton’s time, every measurable example of this gravitational force included the Earth as one of the masses. It was therefore impossible to measure the constant, G, without first knowing the mass of the Earth (or vice versa).

The answer to this problem came from Henry Cavendish in 1798, when he performed experiments with a torsion balance, measuring the gravitational attraction between relatively small objects in the laboratory. The value he determined for G allowed the mass and density of the Earth to be determined. Cavendish’s experiment was so well constructed that it was a hundred years before more accurate measurements were made.

The gravitational attraction between a 15 gram mass and a 1.5 kg mass when their centers are separated by a distance of approximately 46.5 mm (a situation similar to that of the Gravitational Torsion Balance) is about 7 x 10-10 Newtons. If this doesn’t seem like a small quantity to measure, consider that the weight of the small mass is more than two hundred million times this amount.

The enormous strength of the Earth’s attraction for the small masses, in comparison with their attraction for the large masses, is what originally made the measurement of the gravitational constant such a difficult task. The torsion balance (invented by Charles Coulomb) provides a means of negating the otherwise overwhelming effects of the Earth’s attraction in this experiment. It also provides a force delicate enough to counterbalance the tiny gravitational force that exists between the large and small masses. This force is provided by twisting a very thin beryllium copper ribbon.

The large masses are first arranged in Position I, as shown in Figure 1, and the balance is allowed to come to equilibrium. The swivel support that holds the large masses is then rotated, so the large masses are moved to Position II, forcing the system into disequilibrium. The resulting oscillatory rotation of the system is then observed by watching the movement of the light spot on the scale, as the light beam is deflected by the mirror.

Continued from Cycle-1….
SET UP

1. Put the rod in the rod stand. Attach the Heat Engine to the rod by sliding the Heat Engine’s rod clamp onto the rod. The Heat Engine should be oriented with the piston end up and the Heat Engine should be positioned close to the bottom of the rod stand (see Figure 1).

2. Attach the Rotary Motion Sensor to the top of the rod stand and align the medium groove of the pulley of the Rotary Motion Sensor so a string coming from the center of the Heat Engine’s piston platform will pass over the pulley.

Figure 1– Setup

3. Thread one end of a piece of string through the hole in the top of the piston platform and tie that end of the string to the shaft of the piston under the piston platform. See Figure 2. Pass the other end of the string over the medium step of Rotary Motion Sensor pulley and attach the mass hanger and masses totaling 35 grams. This mass acts as a counterweight for the piston.

3. Thread one end of a piece of string through the hole in the top of the piston platform and tie that end of the string to the shaft of the piston under the piston platform. See Figure 2. Pass the other end of the string over the medium step of Rotary Motion Sensor pulley and attach the mass hanger and masses totaling 35 grams. This mass acts as a counterweight for the piston.

4. Position the piston about 2 or 3 cm from the bottom of the cylinder and attach the tube from the can to one port on the Heat Engine and attach the tube from the pressure sensor to the other port on the Heat Engine.

5. Connect the Pressure Sensor to Channel A, the two Temperature Sensors to Channels B and C, and the Rotary Motion Sensor to Channels 1 and 2 on the computer interface.

Figure 2–Attaching string to piston

6. Put hot water (about 80oC) into one of the plastic containers (about half full). Put ice water in the other plastic container. The large (about 3 liter) containers keep the hot and cold temperatures constant during the heat engine cycle.

7. Place one temperature sensor in the hot water and place the other temperature sensor in the cold water. Note that the temperature sensors are labeled hot and cold in the software program so you will have to pay attention to which sensor you put in the hot water and which is in the cold water.

INTRODUCTION

A heat engine is a device that does work by extracting thermal energy from a hot reservoir and exhausting thermal energy to a cold reservoir. In this experiment, the heat engine consists of air inside a cylinder which expands when the attached can is immersed in hot water. The expanding air pushes on a piston and does work by lifting a weight. The heat engine cycle is completed by immersing the can in cold water, which returns the air pressure and volume to the starting values.

THEORY

The theoretical maximum efficiency of a heat engine depends only on the temperature of the hot reservoir, TH, and the temperature of the cold reservoir, TC. The maximum efficiency is given by

Where W is the work done by the heat engine on its environment and QH is the heat extracted from the hot reservoir.

At the beginning of the cycle, the air is held at a constant temperature while a weight is placed on top of the piston. Work is done on the gas and heat is exhausted to the cold reservoir.

The internal energy of the gas (?U=nCv? T) does not change since the temperature does not change. According to the First Law of Thermodynamics, (?U=Q _ W) where Q is the heat added to the gas and W is the work done by the gas.

In the second part of the cycle, heat is added to the gas, causing the gas to expand, pushing the piston up, doing work by lifting the weight. This process takes place at constant pressure (atmospheric pressure) because the piston is free to move.

For an isobaric process, the heat added to the gas is QP=nCP?T, where n is the number of moles of gas in the container, CP is the molar heat capacity for constant pressure, and ?T is the change in temperature. The work done by the gas is found using the First Law of Thermodynamics, W=Q-?U, where Q is the heat added to the gas and U is the internal energy of the gas, given by ?U=nCV?T, where CV is the molar heat capacity for constant volume.

Since air consists mostly of diatomic molecules, CV=5/2 R and CP=7/2 R.

In the third part of the cycle, the weight is lifted off the piston while the gas is held at the hotter temperature. Heat is added to the gas and the gas expands, doing work. During this isothermal process, the work done is given by

where Vi is the initial volume at the beginning of the isothermal process and Vf is the final volume at the end of the isothermal process. Since the change in internal energy is zero for an isothermal process, the First Law of Thermodynamics shows that the heat added to the gas is equal to the work done by the gas:

In the final part of the cycle, heat is exhausted from the gas to the cold reservoir, returning the piston to its original position. This process is isobaric and the same equations apply as in the second part of the cycle.