TAP207 0 Projectile Motion
TAP207 0 Projectile Motion
TAP207 0 Projectile Motion
This episode looks at the independence of vertical and horizontal motion. It concerns objects
accelerating vertically when projected horizontally or vertically. The crucial concept is that vertical
acceleration does not affect horizontal velocity. This explains all projectile motion. You can
discuss why this is the case dynamically but this is best left until later in the study of mechanics.
Getting the basic concept across should be your priority. Similarly, make it clear that you are
ignoring any effects of drag at this stage.
(Note that a projectile is an object which is initially projected by a force, but which then continues
to move freely under the influence of gravity; a rocket which is firing its motors is not a projectile.)
Summary
Demonstration and discussion: Motion in a parabola. (10 minutes)
Demonstration: Monkey and hunter (10 minutes)
Demonstration: Pearls in air. (5 minutes)
Student investigation: Range of a projectile. (30 minutes)
Student experiment: Gravity and archery. (30 minutes)
Demonstration + Discussion:
Motion in a parabola
Here are two quick demonstrations showing motion in a parabola.
The first is a quick, fun demonstration that focuses the students minds on parabolic motion. This
is something we all know but this episode is all about explaining the motion. Follow this with the
diluted gravity demonstration.
Having successfully obtained a parabola the following tasks can be used to move the students
understanding forward:
Describe the motion, as precisely as possible, in words. (No hand waving!)
If this proves difficult try breaking up the motion into horizontal and vertical components. What is
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happening to the vertical velocity? (Its decreasing, then changing direction and increasing, i.e.
vertical acceleration.) What about the horizontal velocity? (Its constant.)
Further pointers: Ignoring air resistance, is anything resisting the horizontal motion? (No!)
Will the acceleration due to gravity be different for a horizontally moving object? (No, again!)
You can use Multimedia Motion to generate a graph of projectile motion which clearly shows the
independence of horizontal and vertical velocities.
The discussion should develop the ideas of independence of horizontal and vertical motion and
uniform horizontal velocity and uniform vertical acceleration. Hence, horizontal and vertical
displacements are given by:
sh = vht and sv = uv t + 1/2 a t2. In many cases uv is zero.
Demonstration:
Monkey and hunter
The idea that vertical and horizontal motions can be considered separately is demonstrated in a
dramatic fashion in the classic monkey and hunter experiment.
You need to set this up in advance and check that it is working. When it does work it is a superb
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5
(resourcefulphysics.org
)
illustration. Questioning should focus on why this demonstrates independence of horizontal and
vertical motion both objects have fallen the same distance in the same time.
Demonstration:
Pearls in air
Water droplets also follow a parabolic path in the air. This gives another clear demonstration of
the effect. Again, concentrate on the explanation in terms of independence of horizontal and
vertical motions.
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DC
(resourcefulphy
sics.org)
Student investigation
Here is an interesting approach to projectile motion in which students fire a marble towards a
target. This gives students, working independently or in pairs, an opportunity to design a simple
experiment that will give them practice using the SUVAT equations.
The students should begin by considering vertical motion. If they set their launcher x metres
above the sand pit, the time the ball will be in the air can be found from:
sv = uv t + 1/2 a t 2
From the horizontal range, the horizontal velocity can be calculated. This value can be used to
predict the range when the height above the pit is changed to 2x, 3x, 4x and so on.
A table can be constructed with the following headings:
Height / m
Calculated time
in air / s
Predicted
range / m
3
Measured range
/m
This can be completed for homework it gives useful practice in SUVAT. Graphs can be
constructed of predicted and measured ranges against height. Students should comment on the
comparison between predicted and measured ranges.
Student experiment:
Gravity and archery
Keen students can extend the investigation to consider the effect of gravity in the sport of archery.
overhead projector
screen
small ball
some practice
What to do
1.
para bola
2.
Project the image of a parabola onto a screen and throw the ball so that its shadow
follows the same path.
For success, lob the ball as if trying to land it on an imaginary 'shelf' at the top of the parabola.
Practical advice
This demonstration is an eye-catching way to show that the path of a thrown ball really is
parabolic. Note that the course does not require students to derive or follow the derivation of a
formula for the motion which can be seen to be of the same type as the formula for a parabola.
A good tip to throw the ball successfully is to imagine throwing it to land on a shelf placed at the
top of the parabola.
External references
This activity is taken from Advancing Physics Chapter 9, 130D
Apparatus required:
Drawing board
Carbon paper
White paper
External references
This activity is taken from Resourceful Physics http://resourcefulphysics.org/
electromagnet
iron can
power supply, 12 V
blowpipe tube
ball bearing
4 mm leads
pea shooter
aluminium foil
with notch cut out
electromagnet
blow
XX
XX
steel can
power pack
You may well see the two starting their fall together; you are more likely to hear the collision!
Relative motion can be lethal when it causes an unwanted collision. Watch the relative
velocity vector with care.
2.
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Practical advice
All students should see, and hear, this demonstration at some time in their lives. Now it injects a
little life into what might otherwise be a rather dry topic.
Technician's note:
This experiment requires care when setting up. The collision needs to happen before either bullet
or monkey hit the floor, for example. That both start falling at the same time is more likely if the
smallest possible current is used to activate the electromagnet. A little care and knowledge also
helps in designing the circuit breaker. The ball bearing must break the electrical circuit by tearing
the foil. It is necessary to make a slit in the foil to initiate the tear. The crocodile clips must be on a
non-conducting support.
It is probably best to ensure that the barrel of the blowpipe is horizontal, as this simplifies the
discussion.
Alternative approaches
Videos of this event tend to be unconvincing as most equipment does not have a sufficiently high
frame rate.
External references
This activity is taken from Advancing Physics Chapter 9, 170D
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Xenon strobe
Bucket
Low voltage power supply
Be safe
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
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Apparatus required
Constant head apparatus, (a large tin with bung and tube will do. See also
http://www.practicalphysics.org/go/Apparatus_1027.html for more information.)
Bucket
Stroboscope
External references
This activity is taken from Resourceful Physics http://resourcefulphysics.org/
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a protractor
a metre rule
safety spectacles
a compression spring
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You may be given the launcher to assemble or be asked to construct one from drawings.
Removing the nail smartly will result in a clean launch. You will want to measure the angle of
launch and the range and maximum height of the flight.
1.
Design and carry out an experiment to measure the exit speed of the marble for a given
spring compression setting.
2.
Now use the kinematic equations for a given angle of launch, ignoring air resistance, to
see if you can land the marble in the sand pit. Is it reasonable to ignore air resistance
here? Is the marble flight adequately described by the kinematic equations, used in two
dimensions?
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The equations allow you to predict, perhaps surprisingly well, where the marble will land.
2.
At the end of this activity you should be confident in using the equations.
3.
There are some limitations to be careful of when applying the equations to a real
projectile launcher.
Practical advice
The launcher activity will allow your students to get some practical work done while studying
motion in a gravitational field. You may want them to build the launcher themselves or provide a
kit for assembly.
The launcher design described in this activity was based on the beautiful but expensive Pasco
device. Students like to use the equations to get the marble into the sand-pit. Competition soon
sets in.
In trying to measure the muzzle velocity some students might try an indirect approach and you
might revise some energy ideas in the first part of the activity, although this is not strictly
necessary. Most students will be happy with simple conservation arguments from pre-16 course.
Alternative approaches
A more controlled version might be to organise an activity around one pre-made launcher.
Be safe
Students should wear eye protection, at least bearing the 'F' impact code (although 'B' would be
better)' during this activity. The projectiles are small and may well transfer significant amounts of
kinetic energy on impact. For the same reasons you may want to limit the materials and
construction techniques used. Considering the disposition of the firing ranges before live firing
commences may also limit the collateral damage to fixtures and fittings.
External references
This activity is taken from Advancing Physics Chapter 9, 172E
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The archer shoots the arrow horizontally at the 40 m target. How far does it drop over this
range?
2.
How would the archer make allowance for this fall? Think carefully before committing
yourself.
3.
4.
50 years ago the release speed of an arrow was about 30 m s 1. What effect would this
have on the vertical distance the arrow fell? Calculate the drop for a range of 60 m to
check your answer.
5.
We have ignored the effect of air resistance in these calculations. How could you take
account of it? You can explore it most easily by making a computer model of the motion.
Practical advice
An example where vectors and simple kinematics give insight into a phenomenon.
Time of flight
40 m
0.67 s
60 m s 1
Vertical drop
h
1 2
1
2
gt 9.81 m s 2
s
2
2
3
2.2 m
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2.
3.
Similar calculations
4.
h50
1
5
9.81 m s 2
s
2
6
h 60
1
2
9.81 m s 2 1 s 4.9 m
2
3 .4 m
External references
This activity is taken from Advancing Physics Chapter 9, 110s
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