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Think and Talk What is the connection?

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What is the connection? Projectile motion

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What is a projectile?

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**Which equations can be used to describe the motion of projectiles?**

Think and Talk Which equations can be used to describe the motion of projectiles? Use of ShowMe boards for this lesson to check understanding as lesson progresses.

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**What force acts on an upward moving projectile?**

First, think about… Holding the ball stationary, describe its motion. Images from Microsoft Clip Art

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**When the ball is stationary, what forces are acting on it? **

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**What forces are acting on the ball?**

Remove the hands and…? What happens to the ball? What forces are acting on the ball? Air resistance is negligible

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**Explain in terms of forces.**

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?**

The only force acting is the force of gravity. It is a common misconception that another upward force is acting on the ball whilst it is in the air. Images from Microsoft Clip Art

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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? The only force acting is the force of gravity. It is a common misconception that another upward force is acting on the ball whilst it is in the air. Images from Microsoft Clip Art

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**A ball thrown up in the air.**

Is it on its way up or down? The only force acting is the force of gravity. It is a common misconception that another upward force is acting on the ball whilst it is in the air. Images from Microsoft Clip Art

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**…the downward motion will mirror the upward motion.**

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. The only force acting is the force of gravity. It is a common misconception that another upward force is acting on the ball whilst it is in the air. Images from Microsoft Clip Art

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**How will initial vertical velocity and final vertical velocity compare in magnitude?**

In direction? The only force acting is the force of gravity. It is a common misconception that another upward force is acting on the ball whilst it is in the air. Images from Microsoft Clip Art

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**Up or down, what is the acceleration of the ball?**

The only force acting is the force of gravity. It is a common misconception that another upward force is acting on the ball whilst it is in the air. Images from Microsoft Clip Art

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–9.8 m s–2 The only force acting is the force of gravity. It is a common misconception that another upward force is acting on the ball whilst it is in the air. Images from Microsoft Clip Art

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**air resistance is negligible**

Remember: air resistance is negligible The only force acting is the force of gravity. It is a common misconception that another upward force is acting on the ball whilst it is in the air. Images from Microsoft Clip Art

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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? The only force acting is the force of gravity. It is a common misconception that another upward force is acting on the ball whilst it is in the air. Images from Microsoft Clip Art

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**Summarise your learning for a vertical projectile**

Direction of motion Forces Velocity Acceleration Horizontal Vertical On ShowMe boards.

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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 Vertical Air resistance negligible so only force of gravity acting in the vertical Changing with time Constant or uniform acceleration of – 9.8 m s–2 On ShowMe boards.

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**Another projectile situation…**

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**Picture a motorcyclist…**

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**DON’T TRY THIS AT HOME …on the top of a tall building**

about 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.**

On ShowMe boards.

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**Predictions for a horizontal projectile**

Direction of motion Forces Velocity Acceleration Horizontal Vertical On ShowMe boards.

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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 and**

Properties 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 On ShowMe boards.

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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 Vertical Air resistance negligible so only force of gravity acting in the vertical Changing with time Constant or uniform acceleration of – 9.8 m s–2 On ShowMe boards.

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**Class challenge! Can you save the motorcyclist from being eaten?**

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**Do you believe in physics. Do you trust the equations of motion**

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**

Suggest set up such as PASCO mini-launcher with photogates (space 10 cm apart to confirm constant horizontal velocity). 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.

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**sh = uht + ½at2 What formula can be used to calculate**

the horizontal displacement of an object fired horizontally if horizontal velocity and time of flight are known? time of flight (s) horizontal displacement (m) sh = uht + ½at2 horizontal velocity (m s–1)

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**sv = uvt + ½at2 What formula can be used to calculate**

the vertical displacement of an object fired horizontally? time of flight (s) vertical displacement (m) sv = uvt + ½at2 initial vertical velocity (m s–1)

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**Which will hit the ground first?**

Are the two balls identical? Does it matter? Predict, observe, explain

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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 For each time, two individual students calculate and verify.

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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 For each time, two individual students calculate and verify.

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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 For each time, two individual students calculate and verify.

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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

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**The vertical component**

launch velocity (m s–1) θ

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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. The launch velocity could be measured with photogates. Resolve into components and predict where it will land. Measure range of projectile. © PASCO Feedback

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**From the measured range, calculated what the launch velocity should be.**

Are the values the same? Explain! The launch velocity could be measured with photogates. Resolve into components and predict where it will land. Measure range of projectile. © 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 horizontal**

Direction of motion Forces Velocity Acceleration Horizontal Vertical On ShowMe boards.

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**Summarise your learning for a projectile fired at an angle to the horizontal**

Direction of motion Forces Velocity Acceleration Horizontal Air resistance negligible so no forces in the horizontal Constant None Vertical Air resistance negligible so only force of gravity acting in the vertical Changing with time Constant or uniform acceleration of – 9.8 m s–2 On ShowMe boards.

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**Summarise your learning for all projectiles!**

Direction of motion Forces Velocity Acceleration Horizontal Vertical On ShowMe boards.

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**Projectiles at an angle to the horizontal**

Select a velocity and select an angle. Calculate the horizontal and vertical components Will the projectile hit the target? Other resources assMechanics/Projectile/Projectile.swf

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**remember our death-defying motorcyclist?**

A thought experiment… remember our death-defying motorcyclist?

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**What would happen if the building were taller**

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.**

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**This is taken inside an aircraft**

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 microgravity**

© NASA

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**Group challenge! Complete the Weightless Wonder task**

to apply your understanding of equations of motion to a real situation. © NASA

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**What is gravity. What is the force of gravity**

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? Students should establish that they are in fact measuring acceleration due to gravity and accepting that this is the same as gravitational field strength. Suggested methods include simple pendulum method, compound pendulum method, oscillating test-tube of lead shot, free fall, ticker tape used vertically, pulsed water droplets and strobe Guidance can be found on: © NASA

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**Uncertainties in your results**

© NASA

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**What do the results mean? What have you measured?**

Measurement of acceleration due to gravity and acceptance of this being equal in magnitude to gravitational field strength. © NASA

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**Can you measure gravitational field strength directly?**

W = mg using spring balance. © 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 The Soviet Union (USSR) successfully launched the world’s first artificial satellite, Sputnik 1. Sputnik launch Sputnik telemetry

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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 and criteria 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! The NASA mission is taking it into orbit. Students should discuss that this is in fact as a result of the force of gravity – not defying it at all!

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