GRAVITY

This section deals with experiments connected with the acceleration due to gravity (g) - mostly that on the surface of our planet (g = 9.8 m/s²). That means that if an object is dropped near the Earth's surface its speed increases by about 10 ms^-1 every second if the effects of air resistance are ignored.

General theory for the section:
When an object falls from rest and accelerates under the effect of the Earth's gravity the distance it falls (h) in a time t is given by the equation: h = ½ (gt²). The gravitational field strength at the surface of the Earth is approximately 9.81 Nkg^-1 and this will give a mass of one kg an acceleration of 9.81 ms^-2.

When a projectile is thrown it has a constant vertical acceleration (g) towards the ground but a constant horizontal velocity if we ignore air resistance. The horizontal and vertical motions are independent.

In some of the experiments a constant head apparatus is mentioned. This is simply a device for maintaining a constant head of water at an outlet.


1. Mooing milk carton
2. Pearls in air
3. g with a water jet
4. Diluted gravity
5. Diluted gravity - projectile paths
6. g - Gramophone turntable
7. The contracting stream
8. Falling can and water - what happens
9. Diluted gravity again
10. Two balls falling joined by stretched elastic
11. Falling bar for g
12. Vertical acceleration
13. Monkey and hunter
14. Falling can with hole at one side
15. Galileo inclined planes
16. Guinea and feather tube
17. Dropping books and paper - air resistance and drag
18. Floating block in a falling jar
19. Two tennis balls
20. Smiley pop ups

GRAVITY

1. Mooing milk carton

The mooing milk carton can be used as a fun problem to the show the constancy of vertical acceleration in free fall and also to demonstrate g forces. Turn it upside down and drop it in "mid moo". Observe the change in the sound as it goes down. The mooing stops in free fall and starts again when the high deceleration forces occur as it is caught.

Age range : 11-18 depending on treatment

Apparatus required:
Mooing milk carton

2. Pearls in air

(a) This is a classic demonstration designed to show the parabolic path of projectiles in a gravitational field. A water jet is formed by a using the glass part of a dropping pipette fixed to a thin walled rubber tube and connected to the water tap. The rubber tube is passed through an old style ticker timer or over a vibration generator so that the tube is alternately squeezed and released when the device is switched on.

The water jet falls in a parabola from an initial horizontal direction but is also interrupted by the pulsing so that droplets of water are formed instead of a continuous stream. If the arrangement is illuminated with a stroboscope pearl like droplets of water can be made to stand still or move slowly through the air. The constant horizontal velocity and the increasing vertical velocity can be seen by observing the positions of successive drops. To get a permanent record you could make the position of the shadows of the water drops on a screen behind the jet or even photograph it. A truly beautiful demonstration.


(b) An extension of the basic version is what I call the Double Pearls in Air. In this experiment two jets are used from different water taps but with tubes running under the same ticker timer bar. One is adjusted to give a parabola while water simply dribbles out from the other, falling vertically. The vertical acceleration of the drops can then be compared. Of course you can make two parabolas and compare these.




Warnings about pupils and flashing lights should be given here.

Theory:
Since h = 1/2gt² and s= vt the equation for the parabolic path for the water is h = gs²/2v² where s is the horizontal distance travelled, h the vertical distance and v the horizontal velocity of the jet

Age range: 14-18

Apparatus required:
Ticker timer Two water jets Constant head apparatus Bucket Stroboscope

3. g with a water jet

The value of the acceleration due to gravity (g) can be found in a rather novel way by using a jet of water projected horizontally from a dropper attached to a constant head to give a parabolic path. The shape of the path is found by measuring pairs of values of the height fallen (h) and the distance horizontally from the orifice (s) and if the rate of flow of the water is also found the value of g can be calculated. Measure the diameter of the jet to calculate its cross sectional area (A).
The horizontal velocity (v) is obtained from the equation V = Av where V is the volume of water leaving the dropper per second (measure this by directing the jet into a measuring cylinder) and A is the cross sectional area of the jet. Using a TV camera to give an image on the screen or shining light from a projector to make a shadow of the path on a board are both helpful ways of making measurements easier to take.

Theory:
s = vt h = 1/2gt² v = V/pr²

Age range: 16-18

Apparatus required:
Water jet Constant head apparatus Rulers Base clamp Measuring cylinder Stop clock travelling microscope or vernier or TV camera Bucket Mop

4. Diluted gravity

(a) Realising the problem of making accurate measurements of the acceleration due to gravity Galileo diluted gravity by rolling balls down slopes. His original apparatus is in the History of Science Museum, Florence. We can recreate his experiment by rolling a marble down an inclined plastic ramp or tube and measuring the time it takes to travel a measured distance.
It is important to understand that it is much more accurate to measure the small angles by trigonometry than by fiddling around with a protractor! The gravitational acceleration (g) has been "diluted" to g sinA where A is the angle that the tube makes with the horizontal.


Carrying out the experiment by using a rider on a tilted linear air track, I use one 2 m long, can give extremely accurate values for g.

A piece of plastic electrical trunking makes an excellent ramp down which to roll the marbles.

(b) An alternative version of the diluted gravity experiment of Galileo can be performed on a large scale with an aerial ropeway type arrangement fixed across the lab. A wire should be fixed tightly from a high point on one side of the lab to a low point on the other. A small cup either fixed to a pulley wheel or simply tied to a loop of wire can then travel down the wire. Time, distance and angle can easily be measured.

Theory:
Acceleration down the plank or wire = g sinA s = 1/2 gsinA t²

Age range: 14-16

Apparatus required:
Wooden ramp and track or plastic tube Marble Stop clock Ruler Wire Cup and pulley wheel

5. Diluted gravity - projectile paths

An extension of the diluted gravity experiment (see experiment 4) is to investigate a diluted projectile path. Get a drawing board and fix a large sheet of paper to it. On top of this fix a piece of carbon paper - face downwards. Tilt the board and then roll a heavy ball bearing across the top of the paper in a horizontal direction. The path of the ball bearing will be produced on the paper. Different angles of tilt and different path directions can be used. This would be suitable for an introduction to projectiles or at a more advanced level where calculation of the parameters of the paths can be performed.

Age range: 16- 18

Apparatus required:
Drawing board Large ball bearing Carbon paper White paper

6. g - Gramophone turntable

A rather quaint experiment is the use of an old gramophone turntable to measure the acceleration due to gravity (g). The problem with all such measurements is to find a way of determining the time of fall that will always be pretty small over the distances possible in a laboratory. In this method this small time is found by using a gramophone turntable. First fix a piece of tape along a radius. Hold a ball bearing a height h above the rotating turntable and release it at just the moment when the tape passes beneath it. The angle through which the turntable has rotated before the ball bearing hits it is found by either covering the surface with plasticene or a piece of carbon paper over a white sheet of paper.





The period of rotation of the turntable is determined using a stopwatch and may be used to calculate the time of fall (t). The acceleration due to gravity is then worked out using the formula g = 2h/t².
Admittedly it's a very inaccurate method but it does give you a means of getting g and then commenting on why it would be an unreliable answer.


Age range: 16-18

Apparatus required:
Gramophone turntable Large ball bearing
Carbon paper and white paper or plasticene Ruler

6. The contracting stream

The speed of a jet of water falling vertically from a tap into a sink increases the further from the tap it gets. This would seem to suggest that more water reaches the sink every second than is being emitted from the tap. Clearly impossible! This can only be explained if the stream of water gets thinner with increasing depth below the tap. This can be verified by turning the tap on slightly and observing the stream.

7. Falling can and water - what happens

Take a tin can and drill a hole in the bottom. The size isn't critical but two or three millimetres in diameter will be fine. Put your finger over the hole and fill the can with water. Now drop the can - the water stays inside. This is much as you would expect, since all objects accelerate downwards at the same rate if air resistance is ignored. Now repeat the experiment but drop the can after you have allowed some of the water to start streaming out. What happens to the water? It looks as if the can is continuing to empty itself, but this would mean that the water is falling with a greater acceleration than g. This is impossible of course! The can and the water both accelerate at the same rate, g, and the can has the same amount of water in it when it reaches the ground as it had at the start of the drop.

Age range: 14-18

Apparatus required:
Bowl or bucket Tin can with hole

8. Diluted gravity again

Another variation of the diluted gravity experiment is to use a 30 cm long clear plastic ruler that has a groove down its centre, a ball bearing and an overhead projector. Put the ruler on the overhead projector with one end slightly raised (a millimetre or two). (You may need to support the ruler in the middle to stop it bowing).

Now let the ball bearing roll down it - using the image of the ruler on a screen to show the distance reached at certain time intervals. Calculate the acceleration due to gravity as in experiment three.

Age range: 14-16

Apparatus required:
Overhead projector Ball bearing 30 cm clear plastic ruler Stop clock

9. Two balls falling joined by stretched elastic

An interesting problem involving gravity is to take two balls that are joined together by a piece of stretched elastic, and hold one of them so that the other hangs below it - the elastic between them being stretched. Now release them so that they fall. What happens to their separation as they fall? It is worth repeating the experiment with balls of both the same mass and of different masses and trying it with the greater mass at either the top or bottom.

Theory:
The upper ball falls with a greater acceleration than the other - the two are pulled together by the elastic and so the acceleration varies until the elastic becomes slack when they both fall with an acceleration of g

Age range: 16-18

Apparatus required :
Two power balls Piece of elastic

10. Falling helical spring

A variation of experiment nine is to drop an extended helical spring and observe what happens to various parts of it as it falls. You will find that during the drop the bottom coils stay where they are while the upper coils catch up with them and then the whole spring falls together. During the whole motion the centre of mass falls with an acceleration of g. The information that the spring is falling will take a certain time to travel down the spring and so initially the bottom part of the spring "thinks" it is still being held up and so remains at rest.

Using a TV camera to record the fall and looking at a slow motion replay will make the results of both experiments eight and nine much more easy to appreciate.

Age range: 16-18

Apparatus required:
Helical spring TV camera if possible

11. Falling bar method for g

You can use the fact that the vertical acceleration of any point on any rigid falling object is the same no matter whether it is dropped vertically or swung or projected at an angle in the following experiment to find g. A metre ruler is pivoted at one end and held at an angle by a thread fixed to its lower end, the thread being looped over the pivot bar and with a sufficiently heavy pendulum bob tied to the other end. Now burn through or cut the thread. The ball begins to fall and the ruler begins to swing downwards at the same moment. The position where the ball meets the bar can be used to find g. Finding this position can be made easier by putting a piece of carbon paper over a strip of white paper that is fixed to the ruler.

Theory:
Since the ball bearing hits the ruler vertically below the pivot the time taken for the fall will be one quarter of the period of oscillation of the ruler. The period can be found by measuring the time for ten swings of the ruler and then working out the time for one quarter of a swing.

Age range: 16-18

Apparatus required:
Pivoted metre ruler Retort stand and clamp Ball bearing Thread Matches Stop clock Carbon paper White paper

12. Vertical acceleration

The "feel" of the value of the acceleration due to gravity can be gained by putting a small object such as a ball bearing on your hand and then moving your hand downwards. If you move it with an acceleration of less than g the ball bearing stays in contact with your hand but if your hand accelerates with a greater acceleration than g the ball bearing leaves the surface. It is rather more difficult to do this with your hand on top of the object. You can compare this with the loop the loop in a roller coaster or with people in a car going over a bumpy road. You will leave your seat in a car if it travels over the bumps too rapidly.

13. Monkey and Hunter

A monkey hangs from a tree in a jungle and is discovered by a hunter who decides to shoot it. Pointing the rifle between the eyes of the monkey he prepares to pull the trigger. The monkey, being fairly intelligent reasons that if he waits until the moment the bullet leaves the barrel and then drops out of the tree the bullet will pass over his head. The hunter pulls the trigger, the monkey waits until the bullet is leaving the barrel and lets go - to his dismay the bullet hits him directly between the eyes! He was intelligent but had forgotten his Physics!

The explanation for this can be demonstrated by a classic experiment that shows the constancy of acceleration for falling bodies. Mount and electromagnet in a clamp about 0.5 m above the bench and mount a blowpipe horizontally in another clamp so that it is pointing just below the core of the electromagnet. Put a marble in the blowpipe, fix a small strip of aluminium foil across the mouth of the blowpipe and then connect up a series circuit with the electromagnet a d.c power source and the aluminium strip. Switch on and hang a tin from the electromagnet making sure that the blowpipe is pointing at the centre of the tin. Blow sharply down the pipe and the marble will fly out, breaking the foil, causing the tin to fall. The marble will fall at the same rate as the tin and should collide with it before hitting the bench. I have once or twice managed to hit a falling ball bearing. (See water path in a gravitational field)



Age range: 14-18
Apparatus required: Blow pipe Marble Electromagnet Tin lid Aluminium foil Power supply

14. Falling can with hole at one side

The can with holes (see liquid pressure) can be used to demonstrate that if there is no gravitational attraction there will be no liquid pressure. For this experiment use a can with just one hole in one side near the bottom. Fill it with water, cover the hole with your finger and then drop it. Since both can and water fall together there is no net gravitational force and so the water stays in the can.

Theory:
Pressure at a point in a liquid = hrg and since the net value of g is zero for the falling can and water there is no pressure difference between the top and bottom of the water in the can.

Age range: 16- 18

Apparatus required:
Tin can with hole near the bottom Water

15. Galileo inclined planes

An interesting effect of the acceleration along inclined planes can be shown by a variation of Galileo's experiment on diluted gravity. Thread a bead onto each of a set of wires starting at one point on a vertical bicycle wheel from which the spokes have been removed and ending at different points along the circumference. When the beads are released from the top they slide down the wires keeping a circular arrangement and all reaching the end of the chord at the same time. A related problem in gravitation refers to the fact that it takes 42 minutes for objects falling through holes in the Earth to reach the other side whatever chord is used (this is of course a theoretical and ideal situation and ignores all frictional effects!) It would make an ideal and rapid transport system. You can extend the idea to SHM where the body is free to oscillate about the centre of the Earth. Students often find it difficult to accept that the acceleration is zero at the centre of the "fall".

Age range: 16-18

Apparatus required:
Bicycle wheel with spokes removed and wires fitted with beads on them

Both the following two experiments show the effect of air resistance on falling objects.

16. Guinea and feather tube

This is a classic experiment to show the effect of air resistance and the constancy of the acceleration due to gravity. Take a 1 m long glass tube of diameter about 5 cm, put a small piece of feather and a penny into the tube and fit bungs tightly into both ends - one with a metal tube in the centre. Attach the tube to a vacuum pump. Upend the tube and show that the penny falls faster than the feather because it has much lower air resistance. Now pump out the air and show that they both fall at the same rate.

A video clip of astronauts dropping a falcon feather and a hammer on the Moon illustrates this as well. (It is important to realise that on the Moon there is no air but there is still a gravitational field, about 1/6 of that at the surface of the Earth.) It is certainly not true to say that no air means no gravity.

Age range: 11- 14

Apparatus required:
Guinea and feather tube Vacuum pump Coin Feather

Safety consideration – put some sticky tape around the lower few centimetres of the tube to prevent the tube shattering if the penny hits it too hard!

17. Dropping books and paper - air resistance and drag

This is an interesting experiment on air friction but it is important to stop between each part and ask the students what happens next?

(a) Drop a sheet of paper - it falls slowly due to air friction
(b) Now crumple it up - its mass is unaltered but the crumpling reduces the air friction it falls quicker
(c) Then use another similar flat sheet of paper but this time with book on top of it - the effect of the air friction on the paper is removed
(d) Then a sheet of paper with a book underneath it - they both fall together
(e) And finally a ream of loose paper. All the sheets fall at the same rate.
An alternative to parts (c) and (d) is to use a metal disc with a similar sized paper disc placed either on top of it or below it.

These experiments remove the need for the traditional guinea and feather experiment if you don't have a vacuum pump.

Age range: 14-18

Apparatus required:
A stack of loose paper A book of similar area

18. A floating block in a falling jar

A jar about half full of water has a block of wood floating in the water and is suspended from a helical spring. Initially the jar is supported. If the jar is released the water level stays at the same place in the jar and the block floats at the same level as it falls.

Theory:
The depth at which the block floats depends on its weight and the upthrust on it. The upthrust depends on the weight of water displaced and so as the acceleration of the jar and block change BOTH the weight of the block and the upthrust change in the same way – the block floats at the same depth as it falls.

Objects in accelerated frames of reference behave in the same way as they would in gravitational fields. The falling on the spring is subject to a varying acceleration just like it would be if it were taken to the Moon where the gravitational acceleration is less. This is a very useful demonstration of one of the ideas of General Relativity!

Age range: 11-18 depending on the treatment of the theory

Apparatus required: Jar Water Wooden block Helical spring

See also Waves. A further experiment about gravity involves a falling candle and is described in the section on convection (number six).

19. Two tennis balls

Take two tennis balls and inject one with water. (Make sure that it is completely full) The balls will still look identical and if you drop them they will both fall at the same rate.

Ask the pupils why?

They will probably say that they fall at the same rate because they are the same, same size and same weight.
Then asked to hold them to show that objects of different mass still accelerate at the same rate in a gravitational field.
(The injected ball will reseal itself when the needle is withdrawn)

Age range: 11-16

Apparatus required:
Two tennis balls Water Syringe

20. Smiley pop ups and projectile motion

In his book 'Experiments in Physics' Colin Siddons suggested these of small 'pop-up' toys to study projectile motion. This is a really good idea and can form the basis of an investigation at GCSE or A level. The toys, called Smiley Pop Ups, are very cheap (about 35p in 2005) and introduce a little bit of fun into the experiment.

You squash the toy onto the bench and then the rubber sucker slowly comes off and the toy launches itself into the air. Since the same spring is used each time the launching force should be the same. This means that both vertical motion and motion at an angle to the vertical can be investigated. For the angled motion I have used tilted runways or even tilted the lab tables where this has been possible.
Fixing a pin through a piece of sellotape stuck to the ramp or putting a piece of rough paper on the slope will stop the toys slipping down the slope.

Age range: 14-19

Apparatus required:
Smiley pop up (or similar), ruler, ramp, rough paper or pin and sellotape