An Analysis of Projectile Motion Projectile Motion Lab Report
What is the connection? Projectile motion.
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Transcript of What is the connection? Projectile motion.
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What is the connection?
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Projectile motion
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Which equations can be used to describe the motion of projectiles?
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What force acts on an upward moving projectile?
First, think about…
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When the ball is stationary, what forces are
acting on it?
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Remove the hands and…?
What happens to the ball?
What forces are acting on the ball?
Air resistance is negligible
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Describe the motion using the words velocity,
acceleration and displacement.
Explain in terms of forces.
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Sketch the velocity–time and acceleration–time
graphs of the motion.
Include values on the axes.
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What force acts on an upward moving projectile?
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Initial vertical velocity of a ball dropped from a height?
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A ball thrown up in the air.
Vertical velocity at maximum height?
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A ball thrown up in the air.
Is it on its way up or down?
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For a ball which is thrown up and allowed to fall back to exactly the same point…
…the downward motion will mirror the upward motion.
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How will initial vertical velocity and final vertical velocity compare in magnitude?
In direction?
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Up or down, what is the acceleration of the ball?
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–9.8 m s–2
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Remember:
air resistance is negligible
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Describe the horizontal motion of this tennis ball.
Are there horizontal forces acting on the ball?
Does the horizontal velocity change?
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Summarise your learning for a vertical projectile
Direction of motion
Forces Velocity Acceleration
Horizontal
Vertical
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Summarise your learning for a vertical projectile
Direction of motion
Forces Velocity Acceleration
Horizontal
Air resistance negligible so no forces in the horizontal
Constant (in this case 0 m s–1)
None
VerticalAir resistance negligible so only force of gravity acting in the vertical
Changing with time
Constant or uniform acceleration of – 9.8 m s–2
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Another projectile situation…
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Picture a motorcyclist…
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…on the top of a tall buildingabout to perform a death-defying stunt of incredible skill.
DON’T TRY THIS AT HOME
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Predict her path once she launches off the building.
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Predictions for a horizontal projectile
Direction of motion
Forces Velocity Acceleration
Horizontal
Vertical
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Just as she launches…someone switches off gravity!
Predict her path with no gravity.
Remember: air resistance is negligible.
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Switching gravity back on…
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Virtual Higher Physics → Mechanics andProperties of Matter → Projectile Motion→ Video of projectile motion
(Motion Grapher Simulations:ball projected horizontally (horizontal component)ball projected horizontally (vertical component))
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Summarise your learning for a horizontal projectile
Direction of motion
Forces Velocity Acceleration
Horizontal
Vertical
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Summarise your learning for a horizontal projectile
Direction of motion
Forces Velocity Acceleration
Horizontal
Air resistance negligible so no forces in the horizontal
Constant None
VerticalAir resistance negligible so only force of gravity acting in the vertical
Changing with time
Constant or uniform acceleration of – 9.8 m s–2
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Class challenge!
Can you save the motorcyclist from
being eaten?
http://www.absorblearning.com/media/attachment.action?quick=ww&att=2357
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Do you believe in physics?Do you trust the equations of
motion?Would you jump over the crocodiles based on the
equations?
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Verifying the equations of motion
How could you use the equipment to verify the
equations of motion?
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Okay then…some hints
What determines the horizontal displacement?
What determines the time spent in the air?
What is the initial vertical velocity of a
horizontal projectile?
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Class challenge
Use the equipment to determine the horizontal velocity with which the ball leaves the launcher.
Safety warnings
(c) Pasco Feedback
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Class challenge
How well have you understood?
Calculate the horizontal velocity
required to save the motorcyclist from
being eaten.
http://www.absorblearning.com/media/attachment.action?quick=ww&att=2357
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What formula can be used to calculate
the horizontal displacement of an object
fired horizontally if horizontal velocity
and time of flight are known?
sh = uht + ½at2 horizontal displacement (m)
horizontal velocity (m s–1)
time of flight (s)
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What formula can be used to calculate
the vertical displacement of an object
fired horizontally?
sv = uvt + ½at2 vertical displacement (m)
initial vertical velocity (m s–1)
time of flight (s)
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Which will hit the ground first?
Predict, observe, explain
Are the two balls identical?Does it matter?
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A thought experiment: the frictionless marble on the
frictionless surface
The marble is travelling horizontally at 5 m s–1. Describe its motion at:
0.1 s, 0.2 s, 0.3 s, 0.4 s, 0.5 s, 0.6 s, 0.7 s, 0.8 s, 0.9 s, 1.0s
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A thought experiment: the frictionless marble on the
frictionless surface
How can we calculate the horizontal displacement at:
0.1 s, 0.2 s, 0.3 s, 0.4 s, 0.5 s, 0.6 s, 0.7 s, 0.8 s, 0.9 s, 1.0s
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The frictionless marble dropped off the Eiffel Tour (into the air-resistance-free Paris sky)
How can we calculate the vertical displacement at:
0.1 s, 0.2 s, 0.3 s, 0.4 s, 0.5 s, 0.6 s, 0.7 s, 0.8 s, 0.9 s, 1.0s
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The frictionless marble:the complete picture
Using Excel, we can plot a graph of
horizontal displacement against vertical
displacement.
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Observe and explain
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Still don’t believe the independence of horizontal and
vertical components?
Two more possibilities…
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A traditional method involving:
• five small cans, open at each end• (take care of sharp edges)• a white board with graph paper (traditional not • interactive)• a method of fixing cans to the board.• a ball• a good aim.
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Position the cans so the ball, when projected horizontally, will fall through each can.
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A higher technology method involving:
The photo shown above must have been faked. Explain!© Pasco Feedback
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Group thinking
What do you already know that you can apply to projectiles fired at an angle?
Think forces, vectors, equations…
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© PASCO Feedback
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Hints!
Any vector can be
resolved into its
horizontal and vertical
components.
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The horizontal component
launch velocity (m s–1 )
θ
cos
cos
component launch velocity cos
adjacent
hypotenuse
adjacent hypotenuse
horizontal
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The vertical component
launch velocity (m s–1 )
θ
sin
sin
sin
opposite
hypotenuse
opposite hypotenuse
vertical component launch velocity
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Calculate the launch velocity.
Using this, resolve the vectors and calculate the range of the projectile.
The range is how far the projectile travels horizontally.
© PASCO Feedback
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From the measured range, calculated what the launch velocity should be.
Are the values the same?
Explain!
© PASCO Feedback
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Predict, then determine experimentally and by calculation which angle will give the greatest range for a fixed launch velocity.
© PASCO
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Summarise your learning for a projectile fired at an angle to the
horizontalDirection of motion
Forces Velocity Acceleration
Horizontal
Vertical
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Direction of motion
Forces Velocity Acceleration
Horizontal
Air resistance negligible so no forces in the horizontal
Constant None
VerticalAir resistance negligible so only force of gravity acting in the vertical
Changing with time
Constant or uniform acceleration of – 9.8 m s–2
Summarise your learning for a projectile fired at an angle to the
horizontal
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Summarise your learning for all projectiles!
Direction of motion
Forces Velocity Acceleration
Horizontal
Vertical
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Projectiles at an angle to the horizontal
http://www.absorblearning.com/media/attachment.action?quick=wx&att=2359
Select a velocity and select an angle.
Calculate the horizontal and vertical components
Will the projectile hit the target?
Other resourceshttp://www.helpmyphysics.co.uk/projectile.htmlhttp://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/ClassMechanics/Projectile/Projectile.swf
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A thought experiment… remember our death-defying motorcyclist?
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What would happen if the building were taller? And the horizontal velocity greater?
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And if the Earth’s surface curved away more steeply?
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This is what Newton thought about, sometime between 1643
and 1727.
http://www.smaphysics.ca/phys40s/field40s/newtmtn.html
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This is taken inside an aircraft. Explain why these NASA trainee astronauts (class of 2004) appear weightless.
© NASA
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Watch the clip on microgravityhttp://microgravityuniversity.jsc.nasa.gov/theProgram/video/video.cfm
© NASA
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Group challenge!
Complete the Weightless Wonder task
to apply your understanding of
equations of motion to a real situation.
http://www.nasa.gov/audience/foreducators/topnav/materials/listbytype/Exploring_Space_Through_Algebra_Weightless_Wonder.html
© NASA
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What is gravity?What is the force of gravity?
What are the effects of gravity?What do we know about gravity?How can we make use of gravity?
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Investigating the force of gravity on Earth
Using classroom resources, investigate how
you could measure the gravitational field
strength on Earth.
What are you measuring?
How are you measuring it?
What does it mean?
© NASA
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Uncertainties in your results
© NASA
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What do the results mean?What have you measured?
© NASA
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Can you measure gravitational field strength directly?
© NASA
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Making use of the force of gravity
Newton’s thought experiment of 300 years ago
became a reality on 4 October 1957.
The Soviet Union (USSR) successfully
launched the world’s first artificial satellite,
Sputnik 1.
http://history.nasa.gov/sputnik/sputnik.wav
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Researching physics
What was the significance of Sputnik’s launch,
more than 50 years ago?
What impact has the space race and our ability
to launch satellites into space had on life on
Earth?
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Topics for researching
• The historical aspects of the space race and its significance to humankind.
• Low orbit and geostationary satellites.
• Satellite communication and surveying.
• Environmental monitoring of the conditions of the atmosphere.
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Scientific communication andcriteria for assessment
Another opportunity to build skills for
researching physics units.
Insert more information once released!
Quality sources for research.
Communication of understanding, including
summarising information in own words.
Scientific content within communication.
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Reviewing our learning
In this section, we have developed our
understanding of motion to build from vertical
projectiles, to horizontal projectiles and projectiles at
an angle.
We have followed the thought processes of Sir
Isaac Newton through to the very first successful
launch of a satellite, and considered how scientific
developments impact on life on Earth.
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A final thought…This paragraph is taken from an article about a
sample of wood being taken on a NASA
mission to orbit Earth.
A piece of Sir Isaac Newton's apple tree will
‘defy’ gravity, the theory it inspired, when
it is carried into space on the next Nasa
shuttle mission. © BBC News website
Discuss!