Projectile Motion
Forces and Motion

Components of motion

for 14-16

Forces and their effects can be superimposed. The path of any projectile combines horizontal constant speed with vertical acceleration due to gravity. As Galileo showed, the independence of vertical and horizontal motions provides a route to simple analysis. But the independence of these two motions is counterintuitive. Only careful teaching, combined with demonstration experiments, will convince students.

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A toy car with two motions

Projectile Motion
Forces and Motion

A toy car with two motions

Practical Activity for 14-16

Class practical

This experiment reinforces the x and y directions convention, and the use of vector arrows. It also shows that a motion can have different components.

Apparatus and Materials

For each student or student group

  • Toy car
  • Transparent plastic sheet
  • Board or other suitable surface marked with grid lines

Health & Safety and Technical Notes

Read our standard health & safety guidance


The plastic sheet should be thick enough to prevent crumpling as it moves.

For grid lines, a spacing of 5 centimetres is adequate. Depending on student ability, it may be better if you prepare these before the lesson. Some students may be uncertain about " x direction" and " y direction". Label them on the boards.

Procedure

  1. On a sheet of paper, draw a grid that is a smaller version of the one under the plastic sheet. This is a map of the grid.
  2. Put the plastic sheet over the grid lines.
  3. Push the car steadily across the sheet in the x direction.
  4. On your map, mark the start and finish positions of the car. Draw a straight line that joins the starting and finishing positions. Draw an arrowhead on the line, with its point at the finishing position.
  5. With the car stationary on the sheet, pull the sheet in the y direction at a constant speed. Mark the start and finish positions on the map.
  6. Now one person should move the car in the x direction across the plastic while another person drags the plastic sheet in the y direction. Drag it as smoothly as you can, and not too fast. Don't let the car wheels skid.
  7. You should find that the car has ended up at a different place on the grid. That is because it has two motions. It has the motion you give it by pushing it, and the motion it gets from the moving plastic sheet. Make a new map of the grid. Mark the starting and finishing positions, and join them with a journey arrow as you did before.
  8. You tried to push the car in the x direction. Draw an arrow to show what the motion would have been like if the plastic sheet had stayed still.
  9. The sheet moved in the y direction. Draw an arrow, starting in the same place as the others, to show the journey of the plastic sheet.
  10. Repeat this, but change the velocity of the car and/or the plastic sheet. You'll need to make a new map grid for each journey. Draw three arrows again, one for the x -direction motion, one for the y -direction motion, and one for the combined motion.
  11. Decide what pattern the arrows make.
  12. You can try all sorts of different combinations of motion of the car and the sheet. To keep it simple to start with, try changing only the direction in which you push the car. Try pushing it in the opposite direction to its original journey (in the negative x direction). Then try moving the car and the sheet in the same direction. Always follow the rule that the car must never skid.

Teaching Notes

  • This can be as open-ended as you like. You could limit investigation to perpendicular motions, and guide students to the idea that the combined motion is shown by the diagonal of the rectangle that the separate motions make. Or students could try both perpendicular motions and co-linear motions, for which the resultant motion is a simple sum.
  • They could try a wider range of orientations of motions, but it becomes more difficult to see that the resultant is shown by the diagonal of a parallelogram.

This experiment was safety-tested in March 2005

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Independence of vertical and horizontal motions

Projectile Motion
Forces and Motion

Independence of vertical and horizontal motions

Practical Activity for 14-16

Class Practical

This is a simple experiment showing a difficult idea: that time of fall is unaffected by any horizontal motion.

Apparatus and Materials

  • Stones

Health & Safety and Technical Notes

Whether the activity is done inside or outside, only do this experiment with students that you can trust using stones as projectiles.

Do this in a place where stones will land on soft ground and not shatter or bounce.

Read our standard health & safety guidance


There are many ingenious trigger devices for launching horizontal and vertical balls at the same time. They are normally based on one ball rolling down a ramp to hit a stationary ball at the end of the ramp. Both balls have the same mass and so their momentum is exchanged and the rolling ball falls vertically downwards and the once stationary ball follows a parabolic path.

Do the experiment in the open, if possible.

Procedure

  1. Drop two stones vertically from the same height, one from each hand. Practice releasing them at the same time. Listen for them hitting the ground. They should land at the same time.
  2. Repeat, but give one of the stones a horizontal motion by moving one of your hands sideways as you let go.
  3. Repeat, but throw both stones out sideways with different velocities.
  4. Try it with stones of unequal size.
  5. Try dropping both stones from lower down or even from an open window or staircase.
  6. Try increasing the horizontal speed of the stone.
  7. The motion could be recorded using a video camera.

Teaching Notes

  • Different masses fall in the same time, with the same vertical acceleration.
  • The key point is that the fall of a stone from a particular height to the ground takes the same time whether or not it also has horizontal motion.
  • The independence of the horizontal and vertical motion enabled Galileo to examine the horizontal motion of projectiles free from any accelerating force. This gave him an indirect way of observing motion when there was no force acting on the object. Hence he understood what later became known as Newton's first law.

This experiment was safety-tested in March 2005

  • A different experiment also shows this, Monkey and Hunter:

Up next

Testing projectile motion with a drawn parabola

Projectile Motion
Forces and Motion

Testing projectile motion with a drawn parabola

Practical Activity for 14-16

Demonstration

This is a demonstration which shows that motion can be predicted.

Apparatus and Materials

  • Object, small

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Draw a rough parabola by sketching vertical and horizontal lines on a blackboard or whiteboard (see diagram).
  2. Throw a small object in a vertical plane parallel to the blackboard and near it, so that it follows the curve. With the proper start, the object follows surprisingly well. It is better to start with a parabola which results from throwing the object horizontally.

Teaching Notes

  • After trying horizontal projection, you could be more adventurous and try the more elaborate path of a complete parabola (see below). Give the object an initial velocity which has both horizontal and vertical components.
  • Discuss how you managed to draw such a perfect parabola, using the idea that the resulting motion for the horizontal (x=vt) and vertical (y =½ at 2 ) components of the motion is a parabola.
  • Their velocity at each instant is a tangent to the parabolic path. The components of a velocity add as vectors.

This experiment was safety-tested in March 2005.

  • A related experiment (Monkey and Hunter) shows that the horizontal and vertical motions of a projectile are independent of each other:

Up next

Multiflash photographs of projectiles

Projectile Motion
Forces and Motion

Multiflash photographs of projectiles

Practical Activity for 14-16

Demonstration

More evidence of Galileo’s insight: that.

Apparatus and Materials

  • Steel ball (2.5 cm in diameter is ideal)
  • Camera and multiflash system
  • Retort stand and boss
  • Lamp, 500 W

Health & Safety and Technical Notes

Read our standard health & safety guidance


For details of specific methods and for general hints:

Multiflash Photography


You will need a grid made of equally spaced horizontal and vertical lines. Position this so that it is in the background when the camera operates.

Procedure

Making the image

  1. Set up the multiflash system.
  2. Start the camera and multiflash system and then launch the ball by rolling it along the bench, so that it rolls off.
  3. Analyzing the image
  4. Use the horizontal and vertical scales to compare the horizontal and vertical spacings of the ball images.
  5. Describe what happens to the horizontal spacings between each position of the ball.
  6. Describe how the vertical spacings change.

Teaching Notes

  • Students should see that the horizontal spacings are constant, since the horizontal velocity is constant. They should see that the vertical spacings increase according to s=1/2 at 2, since the vertical velocity increases as the ball accelerates downwards.
  • The two motions have different causes and behave differently. It is valid and useful to consider them separately.
  • Galileo realized this and used the idea to analyze cannonball motion. This revolutionized ‘ballistics’ and hence warfare.
  • You could repeat this using a ball showing:
    • Vertical motion of a ball bearing
    • Horizontal motion along a bench at constant speed
    • Projectile motion of a ball bearing thrown out horizontally
    • Two ball bearings released simultaneously; one to perform vertical motion and the other thrown horizontally to follow parabolic projectile motion.
  • Analyze the photographs by transferring the motion to an overlaid grid (e.g. a sheet of acetate). Mark the positions of the ball bearing on the sheet and then draw lines horizontally and vertically through the ball bearing positions.
  • Check the vertical motion for constant acceleration (the horizontal lines are spaced from the top in intervals of 1:4:9:16 ...). Check the horizontal motion for constant speed (the vertical lines are equally spaced).
  • To calculate the acceleration due to gravity: measure the average speed of the ball bearing near to the beginning of its motion and near to the end. Divide the time taken between these two calculations, i.e. from the centre of the space between the two positions of the ball bearing for which the average speed was calculated in the first position. (It will be the time for one less flash than the number of images between the first ball position measured and the last.)

This experiment was safety-tested in March 2005

  • A different experiment (Monkey and Hunter) shows that horizontal and vertical motions of a projectile are independent of each other:

Up next

The apple and arrow experiment

Projectile Motion
Forces and Motion

The apple and arrow experiment

Practical Activity for 14-16

Demonstration

This lovely demonstration, which can be difficult to set up, shows that two objects which start to fall from the same height at the same time always have the same height as they fall.

Apparatus and Materials

  • Dynamics trolley, spring loaded, with rod ‘trigger’ for spring release
  • Grooved launching ramp with fixed bulldog clips
  • Launching platform (a drawing board or other plank of wood)
  • Variable voltage supply
  • Coil (120 turns) and C-core for coil, or other electromagnet that will hold and quickly release the can
  • Clamp and stand
  • 'Tin’ can (about 10 cm diameter)
  • Connecting leads, 2.5 m with crocodile clips
  • G-clamps
  • Marble
  • Aluminium foil, thin
  • Ammeter (0 - 1 amp), DC

Health & Safety and Technical Notes

Beware of overheating the wires: limit the current through the coil to 0.7 A.

Wear goggles in case of ricochets.

Read our standard health & safety guidance


For those poor at aiming use a larger can.

It is possible to turn the can on its side and line the can with soft material so that the marble doesn't rebound when it is caught.

Procedure

  1. Fix the launching ramp and dynamics trolley to the launching platform (a drawing board or other plank of wood). Place a small strip of thin aluminium foil between the bulldog clips. To ensure that the foil breaks, nick it so that it is almost cut across. Put the whole arrangement about 1 metre above the bench, fixed horizontally.
  2. The projectile is an ordinary marble. Place it in the groove of the launching ramp, level with the spring of the trolley. On release of the trigger, the spring hits the marble and fires it forward.
  3. The apple is provided by the tin can. To hold it, use the C-core and 120-turn coil. Connect the coil to the variable voltage supply, with the aluminium foil as part of the circuit. The foil will act as a switch when it breaks.
  4. Set up the apple about 2-3 metres in front of the launching ramp. Adjust its height so that the launching ramp is aiming directly at it.

Teaching Notes

  • The demonstration is meant to show that the arrow and the apple both fall equal amounts vertically in the same time. It is essential for students to see clearly beforehand that the arrow is aimed straight at the apple.
  • Do the experiment firing horizontally first. Afterwards you could do it with an inclined launching ramp.
  • You need to show that the apple falls when the circuit is broken, and that the circuit is broken when the marble bullet is fired.
  • It is a good idea to rehearse this experiment two or three times before demonstrating it to a class. The class will probably want to see the experiment repeated.
  • For an alternative firing mechanism, use a pea shooter (some equipment kits contain a pea shooter).

This experiment was safety-checked in March 2005

  • This Apple and Arrow demonstration is also sometimes called Monkey and Hunter:

Up next

Water jet through rings

Projectile Motion
Forces and Motion

Water jet through rings

Practical Activity for 14-16

Demonstration

This experiment shows a stream of water following a parabolic path. It is really impressive to see the water still passing through the hoops even when the rod is tilted.

Apparatus and Materials

  • Glass tube drawn to a jet
  • Wood pole or beam, rigid, at least 2cm long
  • Rings, 3, 10 - 12cm diameter
  • Constant head of pressure apparatus
  • Retort stands, bosses and clamps, 2 (one very tall)
  • Bucket
  • Panel pins
  • Rubber tubing
  • Thread and rubber bands

Health & Safety and Technical Notes

When setting up the constant head tank it will be necessary to take care: use a step ladder rather than climbing on the bench, and have an assistant present to pass things.

Read our standard health & safety guidance


Strap the glass jet securely to one end of the pole or beam so that water emerging from the jet will do so in a direction parallel to the length of the pole.

At equal distances from the end of the jet, hammer pairs of panel pins into the pole or beam as shown.

These pins serve to support the rings by bifilar threads whose lengths between the levels indicated are 15 cm, 60 cm and 135 cm.

Procedure

  1. Mount the beam horizontally near to a sink and connect the jet to the constant pressure head high above the bench.
  2. Turn on the water and adjust its flow rate until a jet of water passes through each of the rings on its way to the sink or bucket.
  3. Tilt the whole device to other angles, showing that the water stream will continue to pass through the rings.

Teaching Notes

  • The pole acts as a tangent to the motion of the water at the jet at its beginning. From that pole the water falls away from its original straight path by the same amount in a given time whatever the tilt. The initial velocity of the water has a horizontal and vertical component; the horizontal component remains unchanged and is independent of the changes in vertical velocity due to gravity.
  • This experiment could be used in preparation for:

    The apple and arrow experiment


This experiment was safety-tested in April 2005

Up next

Estimate of acceleration due to gravity using pulsed water drops

Projectile Motion
Forces and Motion

Estimate of acceleration due to gravity using pulsed water drops

Practical Activity for 14-16

Demonstration

This experiment is one of the most delightful demonstrations in physics and well worth the effort of assembling the equipment.

Apparatus and Materials

  • Constant head of pressure apparatus on tall stand
  • Bucket
  • Xenon stroboscope


  • L.T. variable voltage supply (capable of 8A at 12V)
  • Screen
  • Latex thin walled, small diameter tubing, (not Bunsen tubing)
  • Hoffman clip
  • Ticker-tape vibrator or vibration generator
  • Glass tubing, drawn out to form a stubby jet
  • Tubing adaptor to connect to constant head apparatus
  • Retort stand, boss, and clamp

Health & Safety and Technical Notes

Avoid setting the frequency of the stroboscope near 8 Hz as the flashing light may induce an epileptic fit.

Read our standard health & safety guidance


Set up the apparatus as shown.

This experiment depends mainly on having a good jet. It is easy to draw a glass tube into a jet by heating it in a strong Bunsen flame. The jet is then cut at a point about 2 mm diameter and the end is smoothed by putting it back into the flame for a few seconds. Take care that you do not seal it up. If the stream breaks up into several streams; or fails to break up into drops then other jets should be tried until a good one is found.

Water from a constant pressure supply flows through a rubber tube to the glass jet. Use a Hoffman clip to reduce the flow to a small stream. At the end of the tube there is a short piece of glass tubing drawn out into a jet. The height of the constant pressure supply should be up to 1 m above the jet. Adjust the Hoffman clip so that if the stream is directed vertically upward it rises to a height of 15 cm to 30 cm above the jet.

To make the stream break up into a regular series of drops, place the latex tubing in the vibrator so that the vibrator squeezes it fifty times a second. The Hoffman clip must be located on the rubber tube just before the vibrator so that the pumping action of the vibrator drives water to the jet.

You may want to adjust the flow rate with a Hoffman clip to a suitable value.

Arrange the stroboscope so that it casts a shadow of the stream on the screen. Viewed without the stroboscope, the stream will appear continuous. When the stroboscope is adjusted to the right flashing rate, the stream is seen to be a series of separate drops, which can be frozen in the air and in the shadow cast on a screen.

Procedure

  1. Direct the jet streams in an upward-slanting direction so that one drop in the frozen pattern is exactly at the vertex of the parabola, measurements can be made from that drop, as starting level, downward.
  2. On the shadow measure the vertical distances fallen from the vertex drop to the next below it - and the next and the next.
  3. Use these distances to estimate g , assuming that the time from drop to drop is 1/50 second.
  4. Measure the horizontal separation of the drops.
  5. A photograph can also be taken of the pearls and the shadow (see below) and measurements taken from it using a long time exposure. An acetate sheet placed over the photograph enable the horizontal and vertical lines to be drawn and projected. To avoid scaling problems the screen should be moved until the actual size is projected onto it.
  6. g = 2s/t 2 where s is the distance fallen and t is time.

Teaching Notes

Photograph of pearls in air and their shadow. Photograph courtesy of Brenda Jennison.

  • The pulsed stream of water droplets follows a parabolic path. This happens because:
    • The horizontal motion of water droplets is at constant velocity.
    • The vertical component of motion is a velocity changing at a constant rate due to gravity.
  • You can draw horizontal lines every third pearl for convenience (each pearl may be too crowded). If the distance between the first four pearls is called one unit of distance and all the other grid lines are measured from the top in terms of this distance then you should find that the spacing is in the ratio of 1:4:9:16 showing that for equal intervals of time the pearl drops as the square of the time from the beginning of the fall. (s=1/2 at 2 )
  • For some examples of grids which have been drawn - see below.

This experiment was safety-tested in February 2006

Resources

Download the support sheet / student worksheet for this practical.

Up next

The ‘monkey-and-hunter’ experiment

Projectile Motion
Forces and Motion

The ‘monkey-and-hunter’ experiment

Practical Activity for 14-16

Class demonstration

This demonstration shows that a projectile fired horizontally and an object dropped vertically fall at the same rate. If the monkey had known that, it might have acted differently.

Apparatus and Materials

For the demonstration...

  • Tin (steel) can, decorated to indicate the monkey
  • Tube and small ball (to act as gun and bullet)
  • Electromagnet (e.g. coil and C-core)
  • 2 crocodile clips
  • Strip of thin aluminium foil
  • Low voltage power supply (0-12 V d.c.)
  • Long connecting wires
  • Clamps and stands

Health & Safety and Technical Notes

Read our standard health & safety guidance


Ensure that students are well clear of the area between the gun and the monkey, so that they can see clearly and are unlikely to be hit by a misfired or deflected ‘bullet’. Notes on the equipment:

  • The aluminium foil strip must break readily as the bullet passes through. It can help to cut the strip and press the two free ends together so that they overlap slightly. When the circuit is complete and the current flows, the magnetic field produced will hold the two strips together.
  • To avoid any delay in the dropping of the monkey, reduce the voltage of the supply until the monkey/can is just held in place.
  • The ‘bullet’ should be sufficiently heavy that air resistance does not affect its motion.

Procedure

  1. Set up the electromagnet at a high point at one side of the room.
  2. Connect it in a series circuit with its power supply and the strip of foil. The long connecting wires are needed because the ‘gun’ will be at the opposite side of the room.
  3. Mount the foil strip across the mouth of the tube which acts as a gun.
  4. Ensure that the tube is aligned so that it is pointing directly at the monkey. Ask a student to confirm this alignment.
  5. Switch on the power supply and hang the monkey from the electromagnet. Turn down the current until the monkey just adheres to the magnet. (The monkey must drop as soon as the circuit is broken; any residual magnetism in the coil will delay its release.)
  6. Fire the ‘bullet’ from the gun. This will break the foil, stopping the current to the electromagnet and causing the monkey to drop.

Teaching Notes

  • The key to understanding this demonstration is the idea that both the bullet and the monkey start to fall at the same time. This happens because they both start moving freely under gravity at the same instant. They have the same vertical acceleration g ; the horizontal motion of the bullet is irrelevant.
  • In the film above, the gun is shown pointing horizontally at the monkey. This is not essential, but it is a good way to start. The hunter could be down on the ground while the monkey is on a high branch. Imagine a straight line from the gun to the monkey; as the bullet flies through the air, its downward acceleration pulls it down below this line.
  • After the demonstration, ask the students to suggest how a wiser monkey might have acted.
  • This demonstration is often used as a popular exhibit at open days and school recruitment sessions.
  • Here is a suggested teaching sequence which deals with projectile motion, including the maths of projectiles:

    Projectile Motion


  • The ‘apple-and-arrow’ is a similar demonstration with further information about how to carry it out.

    The apple and arrow experiment


  • The film below shows the procedure for this demonstration.

Up next

Multiflash photography

Conservation of Energy
Energy and Thermal Physics | Forces and Motion

Multiflash photography

Teaching Guidance for 14-16

Multiflash photography creates successive images at regular time intervals on a single frame.

Method 1: Using a digital camera in multiflash mode

You can transfer the image produced direct to a computer.

Method 2: Using a video camera

Play back the video frame by frame and place a transparent acetate sheet over the TV screen to record object positions.

Method 3: Using a camera and motor-driven disc stroboscope

You need a camera that will focus on images for objects as near as 1 metre away. The camera will need a B setting, which holds the shutter open, for continuous exposure. Use a large aperture setting, such as f3.5. Digital cameras provide an immediate image for analysis. With some cameras it may be necessary to cover the photocell to keep the shutter open.

Set up the stroboscope in front of the camera so that slits in the disc allow light from the object to reach the camera lens at regular intervals as the disc rotates.

Lens to disc distance could be as little as 1 cm. The slotted disc should be motor-driven, using a synchronous motor, so that the time intervals between exposures are constant.

You can vary the frequency of ‘exposure’ by covering unwanted slits with black tape. Do this symmetrically. For example, a disc with 2 slits open running at 300 rpm gives 10 exposures per second.

The narrower the slit, the sharper but dimmer the image. Strongly illuminating the objects, or using a light source as the moving object, allows a narrower slit to be used.

Illuminate the object as brightly as possible, but the matt black background as little as possible. A slide projector is a good light source for this purpose.

Method 4: Using a xenon stroboscope

This provides sharper pictures than with a disc stroboscope, provided that you have a good blackout. General guidance is as for Method 3. Direct the light from the stroboscope along the pathway of the object.

In multiflash photography, avoid flash frequencies in the range 15-20 Hz, and avoid red flickering light. Some people can feel unwell as a result of the flicker. Rarely, some people have photosensitive epilepsy.

General hints for success

You need to arrange partial blackout. See guidance note

Classroom management in semi-darkness


Use a white or silver object, such as a large, highly polished steel ball or a golf ball, against a dark background. Alternatively, use a moving source of light such as a lamp fixed to a cell, with suitable electrical connections. In this case, place cushioning on the floor to prevent breakage.

Use the viewfinder to check that the object is in focus throughout its motion, and that a sufficient range of its motion is within the camera’s field of view.

Place a measured grid in the background to allow measurement. A black card with strips of white insulating tape at, say, 10 cm spacing provides strong contrast and allows the illuminated moving object to stand out.

As an alternative to the grid, you can use a metre rule. Its scale will not usually be visible on the final image, but you can project a photograph onto a screen. Move the projector until the metre rule in the image is the same size as a metre rule held alongside the screen. You can then make measurements directly from the screen.

Use a tripod and/or a system of clamps and stands to hold the equipment. Make sure that any system is as rigid and stable as possible.

Teamwork matters, especially in Method 3. One person could control the camera, another the stroboscope system as necessary, and a third the object to be photographed.

  • Switch on lamp and darken room.
  • Check camera focus, f 3.5, B setting.
  • Check field of view to ensure that whole experiment will be recorded.
  • Line up stroboscope.
  • Count down 3-2-1-0. Open shutter just before experiment starts and close it as experiment ends.

Up next

Classroom management in semi-darkness

Interference
Light Sound and Waves

Classroom management in semi-darkness

Teaching Guidance for 14-16

There are some experiments which must be done in semi-darkness, for example, optics experiments and ripple tanks. You need to plan carefully for such lessons. Ensure that students are clear about what they need to do during such activities and they are not given unnecessary time. Keep an eye on what is going on in the class, and act quickly to dampen down any inappropriate behaviour before it gets out of hand.

Shadows on the ceiling will reveal movements that are not in your direct line of sight.

Up next

Two dimensional motion

Projectile Motion
Forces and Motion

Two dimensional motion

Teaching Guidance for 14-16

Galileo was the first to realize that a moving body can have several separate motions, which are independent of each other. His thinking provides a foundation for Newton's treatment of acceleration and force.

A body moving at constant velocity can be described by a sum of velocities in two directions, typically x and y co-ordinates.

The path of a projectile may combine constant speed in the horizontal direction with acceleration due to gravity in the vertical direction. This independence of vertical and horizontal motions is counter-intuitive, and only careful teaching combined with demonstration experiments will convince students.

Accelerations have the same additive properties. They too are vectors that can be added by constructing a parallelogram. Forces too are vectors and obey the same addition rule. In other words: when several forces act on a body, each produces its own effect on motion. One force does not interfere with the motion produced by another force.

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