GOCE
Gravity field & steady state
Ocean
Circulation
Explorer
Free fall
Background Information:
In a vacuum, all objects have the same acceleration due to gravity because
there is no air resistance. Normally a feather takes longer to fall than a
rock because of air resistance, but if they could be dropped from the same
height in a vacuum, they would hit the ground simultaneously. When the only
force acting on an object is its weight, it is said to be in free fall. All objects in free fall have
the same acceleration and this is equal to the gravitational field strength. Astronauts in space
appear to be weightless, because gravity accelerates the craft and the astronauts at the same
rate. They lose contact with the floor of the spacecraft and so no longer feel the floor pushing
them up, but the Earth is still pulling them down. They are not weightless.
F
m
mg
a=
m
a=g
a=
The GOCE satellite will measure the Earth’s
gravity
field
very
precisely
using
accelerometers. In order to produce reliable
readings, the accelerometers’ test masses need
to be kept in perfect free fall at all times. When
GOCE passes over regions of higher density, the
test masses will be pulled down with a greater
force. The amount of force needed to
counteract this pull and to keep the test masses
still can be measured with a very precise Newton
balance.
Learning Objectives:
Pupils understand and can use the terms ‘acceleration due to gravity’, ‘gravitational field
strength’ and ‘free fall’.
Curriculum Links:
Edexcel GCSE in Physics (2109)
P1b 12.4: Use the equation W=mg
P1 b 12.11: Use the unit of gravitational field strength — Newton per kilogram (N/kg)
P2 9.5: Use the equation a=(v-u)/t
P2 9.9: Use the equation F=ma
The Twenty First Century Science suite GCSE Physics A (J635)
It is expected that candidates will show an understanding of the physical quantities and will be
able to use them in quantitative work: force, speed, velocity, gravitational field strength
Materials:
Grapes and grapefruit
Tennis ball
Tennis ball with water injected into it
Book and sheet of paper
Guinea and feather in glass tube
Vacuum pump
500 cm3 water bottles with lids
Trays
Half metre rules
Stopclocks
Suggested activities:
Before the lesson starts inject some water into a tennis ball so that it has a greater mass than
normal. Ask the students to predict what will happen if they drop a grape and a grapefruit at the
same time from the same height. Allow them to try for themselves and then discuss what they
observe. Drop the two tennis balls from the same height and ask the students to confirm that
they land at the same time. Allow them to hold the tennis balls to show that all things fall with
the same acceleration due to gravity, independent of mass. Discuss Galileo and relate it to the
Apollo-15 demonstration on the Moon. Play the video clip of the hammer and feather from the
website listed at the end.
Drop a book and piece of paper and discuss why the paper does not accelerate as much as the
book. The small force of gravity on the paper is opposed by the force of air resistance. A similar
force acts on the book from the air, but it is small compared to the force of gravity on the book.
Demonstrate the guinea and feather experiment. Discuss why the feather takes longer to fall.
Remove air from the tube with the vacuum pump and discuss the effect.
Ask the students what will happen if you poke a hole in the bottom of one of the bottles. Then
ask what will happen if the spouting bottle of water is then thrown up in the air.
A The jet shoots out further and faster
B The jet shoots out slower on the way up and faster on the way down
C The jet stops at the top of flight
D The jet comes out slower all the time
E Something else
Ask the students to make a hole in the bottle with a pin. They should cover it with their fingers
to prevent the water escaping. Each group should lift a bottle above their heads and drop it into
the tray provided. Ask the students to describe what happened and discuss why the water stops
exiting the hole. Introduce the term free fall. Discuss astronauts on board space shuttles and
the International Space Station. Make sure they are aware that the astronauts are free falling
around the Earth, but that they are not weightless. If it is convenient, you could ask students to
stand on a set of scales placed in a lift. They could observe the change in reading as it
accelerates downwards. Discuss this in terms of free fall. Discuss the equivalence of the
acceleration due to gravity and the gravitational field strength before carrying out the
experiment below.
Directions to Pupils
1. Hold the half metre rule vertically above your partner’s open thumb and forefinger. Make sure
the bottom of the half metre rule is level with the top of their forefinger.
2. Let go unannounced. Your partner should catch the half metre rule between their thumb and
forefinger.
3. Record in the table the distance the half metre rule fell before it was caught.
4. Repeat four times with the same hand.
5. Repeat the experiment with the other hand.
6. Switch places with your partner and repeat.
7. Calculate your reaction time t for each drop using the equation d= ½gt2, where d is the
distance fallen. Assume g, the acceleration due to gravity, is 9.8 m s-2.
Trial
Distance travelled
(cm) Right hand
Distance travelled
(cm) Left hand
Reaction
time (s)
Right hand
Reaction
time (s)
Left hand
1
2
3
4
5
Average
Questions:
1. Who had the shorter reaction time?
2. At the Equator the acceleration due to gravity is slightly more, since the rotation of the
Earth makes it bulge at the centre. Similarly, the acceleration due to gravity is slightly less at
the poles, where the Earth is slightly flattened. How would your results differ at the Equator
and at the poles?
Extension:
The standard light gate, data logger and dual metal obstructer experiment could also be used to
find the acceleration due to gravity. Alternatively the motion of a falling tennis ball could be
recorded with a digital camera such as BUSBI and analysed using windows moviemaker.
Instructions on how to do this can be downloaded from:
http://www.science3-18.org/index.php?option=com_content&view=article&id=762:motionanalysis&catid=325:physics&Itemid=1007
A modern version of the classical experiment performed by Galileo is available from:
www.schoolphysics.co.uk/age16-19/.../g_linear_air_track.doc.
References/Resources:
The video clip of a hammer and feather being dropped on the Moon:
http://history.nasa.gov/alsj/a15/video15.html#closeout3
Video clip to show the acceleration due to gravity is the same for all objects
http://www.wfu.edu/physics/demolabs/demos/avimov/byalpha/opvideos.html
A video clip on freefall:
http://web.ics.purdue.edu/~mjcarlso/ST/ST007_Free_Fall.m4v
A video clip on freefall:
http://www.davidcolarusso.com/video/newtonian_dynamics.html
Simulations and activities explaining freefall:
Freefall http://www.physicsclassroom.com/Class/newtlaws/u2l3e.cfm
A video clip of a Newton balance in freefall:
http://www.vuw.ac.nz/scps-demos/demos/Mechanics/FreeFallScale/FreeFallScale.htm
Describes another way to demonstrate freefall:
http://www.thenakedscientists.com/HTML/content/kitchenscience/exp/weightless-water/