**1** MECHANICS EXPERIMENTS Introduction to Vectors Grand Prix on Sun Jun 08, 2014 2:39 am

1. Forces

In this experiment the concept of force is introduced. It is established that a single force is never created, they always come in pairs and two objects are always involved. Two force measurers, a set of slotted masses and a plastic bucket are used to show that the pair of forces have equal size. Newton's third Law is defined. Various types of forces are discussed and students identify the forces acting in various situations.

2. Gravity

Mass and weight are discussed and the strength of a gravitational field is defined. The variation of the value of g around the earth's surface is discussed and values for g on the surface of other celestial bodies are quoted. The inverse square variation of gravity with distance is discovered.

3. Introduction to Vectors

Using three pieces of string tied together at one end and a force measure attached to each of the other ends, students find that 3 plus 4 no longer equals 7. Using scale diagrams of the situation students learn that by using the tip to tail method of adding vectors, they obtain the 3 plus 4 equals 5 Newton outcome they observed using the strings. Students learn to resolve vectors into components and the theory is checked using a dynamics cart on a slope. The parallel and perpendiclar components of its weight are determined from a scale diagram and then measured.

4. Grand Prix

Students learn to control vector components by racing a car around a track sketched on graph paper. The car is a dot that moves on the paper. The components can be as big as the student desires but ( there is always a but!), they can only be the same, one more or one less than the previous move. This simple rule causes the car to behave like a real one. It must be driven like a real one along the correct racing line through the corners and will crash like a real one if the brakes are not applied in time. Drivers fight for track position and can block each other etc etc etc.

5. Frames of Reference

In this exercise two cars move parallel to each other and then at right angles to each other. How the motion of one car appears when looking from the other is investigated. The relative velocity equation is discovered and tested by applying it to someone running in the rain. It predicts what everyone does - hold the umbrella at a forward angle because that is the way the rain appears to be falling.

6. Force and Motion in 1-D

This simple experiment of attaching slotted masses to a force measurer and moving it up and down with one hand, helps students understand why objects accelerate, decelerate and move with constant speed. The knowledge gained is applied to a mass oscillating up and down on the end of a spring. one of the difficult concepts for physics students to understand - the idea acceleration can be a maximum value when an object is stationary for an instant, is discussed. The motion of a skydiver before and after the parachute is opened, is studied.

7. Force and Motion in 2-D

Students apply forces to balls rolling on the desk. The speed of the ball and the strength and direction of the force is varied and the final speed and direction of the ball is noted. From the patterns of behaviour, students are asked to predict the direction and strength of the force that will produce a nominated outcome.

8. Motion on Slopes

In this experiment students roll a cart along a flexible plank. The cart has a mechanics/smart pulley attached to it which enables the position, speed and acceleration versus time graphs to be drawn on the PC screen as it rolls. The plank is made to have uphill and downhill slopes with constant, increasing and decreasing gradient. Students relate the shapes of the slopes to the shapes of the three graphs.

9. Running, Walking and Rolling

In this exercise, students investigate the position of their centre of mass, the angle of their body and the point of contact of their feet when walking and running. Why a crouch start is better than an upright one is established. The behaviour of a ball is analysed and the difference between it skidding and rolling discovered. Why a bicycle can be made to accelerate and brake is investigated.

10. Force, Mass and Acceleration

Using two sets of slotted masses, thick cotton, a mechanics/smart pulley, an interface and a PC, students discover the realtionships between acceleration, force and mass. By controlling the size of the masses hanging from the string passing over the pulley, the students can vary the mass and keep the force constant and vary the force and keep the mass constant.

11. Free Fall

The size of air resistance on falling objects is related to their size and speed. The effect of air resistance is related to the object's mass. The conditions are established where air resistance can be ignored. A stroboscopic picture of a falling golf ball is analysed and its speed versus time graph drawn. The acceleration of the ball is determined and related to the strength of gravity. Then the fun starts! Students are challenged to grab a bank note before it drops out from between their fingers. Grab it and its yours is the challenge. After everyone fails, the time for the note to drop out of reach is calculated. Then, reaction time of students is measured using a timer. This is found to be about twice the time of the calculation.

12. Terminal Velocity

In this experiment students investigate the relationships between terminal velcoity, mass and surface area. A mechanics/smart pulley is clamped near the ceiling. A long cotton is passed over the pulley and a 50 g slotted mass tied to each end. The masses hang half way betwen the floor and the ceiling. A piece of A3 paper is attached to one of the masses. When they are released the paper falls smoothly and reaches terminal velocity which is measured by the PC. Adding sheets of paper varies the mass and keeps the area constant. Starting with a large sheet of paper and then folding the sides in varies the area and keeps the mass constant.

13. Sky Diving

Data is given about the vertical distance fallen by a skydiver during the first 20 sec of free fall. Students analyse the data and calculate the speed and acceleration of the diver. They then determine the resultant force on the sky diver and then calculate the magnitude of the air resistance acting on the diver. They then determine the relationship betwen the magnitude of the air resistance and the speed of the diver. This exercise is best done using a spreadsheet.

14. Projectile Motion

Students analyse the vertical and horizontal motion of a multi flash photo of a projectile. The equation is discovered that calculates the range of a projectile in terms of its initial velocity and angle of launch. The difference in the range when a projectile is thrown at various places around the earth is investigated.

15. CircularI Motion

Students use an electric motor mounted on an arm that is attached to a stand. The motor whirls a rubber ball in a circle. By measuring the mass of the ball, the frequency the ball and the heights above the desk of the motor and the ball as it moves, students can determine the relationship between centripetal force and frequency. Three balls with differing mass and three different length connecting lines enable the relationships between centripetal force, radius and mass to be found. The circular motion kit is available from IEC (Australia).

16. CircularII Motion

Students use a mechanics pulley and an accelerometer attached to an interface to log data as the accelerometer rotates on a phonograph turntable (belt removed so it turns freely). This clever arrangement of the equipment enables the results needed to determine the relationship between centripetal acceleration and velocity to be gathered on 15 sec. Analysis is done after exporting the data to a spreadsheet. Changing the position of the accelerometer on the turntable enables the relationship between acceleration and radius to be found very quickly.

17. Motion in a Vertical Circle

In this fun experiment, students calculate the longest period of a bucket of water whirled in a vertical circle that causes the water to just stay in the bucket as it passes overhead. They verify the accuracy of the prediction with a small plastic bucket half full with water.

18. Friction

In this experiment, the relationship between static friction and the normal reaction is investigated. The coefficient of static friction is defined. They discover that the magnitude of the friction is independent of the area of contact.

19. Turning Corners

In this exercise, students analyse the forces acting on a car and the torques they create when turning corners both flat and banked. They discover what causes a car roll over. Students then investigate how an object at an ustable angle can be prevented from falling over if its base is accelerated. This leads to why a person on a bicycle needs to lean over when rounding a corner.

20. Simple Harmonic Motion

In this experiment, students undertake vector analysis of the horizontal components of the centripetal force acting on an object moving with uniform circular motion. The relationship between horizontal force and displacement is established and SHM defined and the equation to calculate the period is developed. The theory is tested using a mass oscillating on the end of a spring. Students then use the same experimental set up as in 'Energy stored in a Spring' to plot the displacement, velocity and acceleration versus time graphs on a PC as the mass oscillates.

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21. Universal Gravitation

In this exercise the equation that calculates the gravitational force between two masses is developed and tested using data of the motion of the planets. It is used to determine the theoretical value of the gravitational field strength of the earth at its surface. Students learn to use the inverse square law to determine the strength of the earth's field at the distance of an orbiting satellite.

22. Motion of the Moon and Planets

In this exercise students analyse data about the motion of the planets to discover Kepler's three laws. They investigate the consequence of the non-constant speed of the earth in its orbit - the variation in the length of the day. The centre of mass of the Earth/Moon system is investigated. Students investigate the motion of the two bodies relative to their centre of mass and discover the centripetal force acting towards the centre of mass is the same for each.

23. Satellites

Students investigate the conditions needed for a satellite to be set up in a stable orbit. The radius and period of a satellite in geosynchronous orbit is determined. The energy need to get a satellite into a geosynchronous orbit is estimated.

24. Feeling Weightless and Tides

Students investigate how objects can be made to appear weightless when in a non-zero gravity environment. They then discover why objects floating in a space shuttle slowly drift apart. This situation is likened to the water on either side of the earth and why tides occur is explained. Students use their new knowledge to determine that the moon has about twice the tidal influence as the sun.

25. Force and Time

In this experiment, students are introduced to the concepts of impulse and momentum. Using light gates and a glider sliding down a sloping air track, it is proved that the impuse given to the glider by gravity is equal to its change in momentum.

26. Collisions in 1-D

Students analyse the strobscopic pictures of the collisions between gliders on an air track. They discover the conservation of momentum, that each glider received the same sized impulse and the same sized force.

27. Newton's Cradle

Students analyse the ball's on the 'executive toy' called Newton's cradle. They discover that conservation of momentum does not explain what is observed - another factor must be at work. They are introduced to the concept of kinetic energy.

28. Force and Distance

In this experiment the students are introduced to the concept of work and shown that it is related to kinetic energy. Using light gates and a glider sliding down a sloping air track, it is proved that the work done on the glider by gravity, is equal to its change in kinetic energy.

29. Collisions in 2-D

Students study the momentum and kinetic energy of two steel balls before and after a collision. One ball is suspended and another rolls down a ramp. After collision they fall to the floor and from where thy land, horizontal components of velocities are determined.

30. Elastic and Inelastic Collisions

Students analyse the data given about elastic and inelastic collisions. Students investigate the momentum and kinetic energy before, during and after the two collisions. The concept of stored energy is introduced.

31. Centre of Mass

Students analyse a multi-flash photo of a collision between two air table pucks. Students determine the position of the centre of mass and discover it moves with constant velocity even though the pucks collided. The students calculate the velocity of each puck relative to the centre of mass and discover that the total momentum is zero in the centre of mass frame of reference.

32. Energy Transfer

Students use a light gate and a PC to measure the speed of a pendulum bob at the bottom of its swing. They calculate the bob's kinetic energy at the bottom and compare it to the calculation of the bob's gravitational potential energy at release.

33. Elastic Potential Energy in Springs

Students use a mechanics/smart pulley connected to an interface to log data when a mass oscillates on the end of a spring. After transferring the data to a spreadsheet, the kinetic energy and changes in elastic and gravitational potential energies are calculated as the mass drops from the top to the bottom of its motion. The total energy of the system is plotted against time. No more letting the mass drop and guessing its position when it stops. The ingenious arrangement of the equipment is very simple and very effective.

34. Power Transfer in Exercise

In this experiment, students estimate how powerful they are when they do step ups, push ups and climb stairs.

In this experiment the concept of force is introduced. It is established that a single force is never created, they always come in pairs and two objects are always involved. Two force measurers, a set of slotted masses and a plastic bucket are used to show that the pair of forces have equal size. Newton's third Law is defined. Various types of forces are discussed and students identify the forces acting in various situations.

*2 retort stands, bossheads and clamps, 2 0-5 N Force Measurers, 2 sets of 500 g slotted masses, Small plastic bucket, Medicine ball Top*2. Gravity

Mass and weight are discussed and the strength of a gravitational field is defined. The variation of the value of g around the earth's surface is discussed and values for g on the surface of other celestial bodies are quoted. The inverse square variation of gravity with distance is discovered.

*0-20 N Force Measurer, 2 1 kg masses Top*3. Introduction to Vectors

Using three pieces of string tied together at one end and a force measure attached to each of the other ends, students find that 3 plus 4 no longer equals 7. Using scale diagrams of the situation students learn that by using the tip to tail method of adding vectors, they obtain the 3 plus 4 equals 5 Newton outcome they observed using the strings. Students learn to resolve vectors into components and the theory is checked using a dynamics cart on a slope. The parallel and perpendiclar components of its weight are determined from a scale diagram and then measured.

*3 0-5 N Force Measurers, String, Ruler, Set square, Dynamics cart, Inclined plane, 0-20 N Force Measurer, 0-1000 g electronic balance**Top*4. Grand Prix

Students learn to control vector components by racing a car around a track sketched on graph paper. The car is a dot that moves on the paper. The components can be as big as the student desires but ( there is always a but!), they can only be the same, one more or one less than the previous move. This simple rule causes the car to behave like a real one. It must be driven like a real one along the correct racing line through the corners and will crash like a real one if the brakes are not applied in time. Drivers fight for track position and can block each other etc etc etc.

*Graph paper**Top*5. Frames of Reference

In this exercise two cars move parallel to each other and then at right angles to each other. How the motion of one car appears when looking from the other is investigated. The relative velocity equation is discovered and tested by applying it to someone running in the rain. It predicts what everyone does - hold the umbrella at a forward angle because that is the way the rain appears to be falling.

*No equipment needed. An umbrella as a prop is useful Top*6. Force and Motion in 1-D

This simple experiment of attaching slotted masses to a force measurer and moving it up and down with one hand, helps students understand why objects accelerate, decelerate and move with constant speed. The knowledge gained is applied to a mass oscillating up and down on the end of a spring. one of the difficult concepts for physics students to understand - the idea acceleration can be a maximum value when an object is stationary for an instant, is discussed. The motion of a skydiver before and after the parachute is opened, is studied.

*0-5 N Force Measurer, Set of 500 g slotted masses, Retort stand, Bosshead and clamp, Spring, 1 kg mass, 0-20 N Force Measurer, G clamp Top*7. Force and Motion in 2-D

Students apply forces to balls rolling on the desk. The speed of the ball and the strength and direction of the force is varied and the final speed and direction of the ball is noted. From the patterns of behaviour, students are asked to predict the direction and strength of the force that will produce a nominated outcome.

*Tennis ball or golf ball, Book Top*8. Motion on Slopes

In this experiment students roll a cart along a flexible plank. The cart has a mechanics/smart pulley attached to it which enables the position, speed and acceleration versus time graphs to be drawn on the PC screen as it rolls. The plank is made to have uphill and downhill slopes with constant, increasing and decreasing gradient. Students relate the shapes of the slopes to the shapes of the three graphs.

*Flexible plank, Stiff board, Bricks/boxes to support hills, Mechanics/smart pulley, Cart, Interface, 0-5 N Force MeasurerPC Top*9. Running, Walking and Rolling

In this exercise, students investigate the position of their centre of mass, the angle of their body and the point of contact of their feet when walking and running. Why a crouch start is better than an upright one is established. The behaviour of a ball is analysed and the difference between it skidding and rolling discovered. Why a bicycle can be made to accelerate and brake is investigated.

*Ruler (30 cm or 1 metre), Tennis ball Top*10. Force, Mass and Acceleration

Using two sets of slotted masses, thick cotton, a mechanics/smart pulley, an interface and a PC, students discover the realtionships between acceleration, force and mass. By controlling the size of the masses hanging from the string passing over the pulley, the students can vary the mass and keep the force constant and vary the force and keep the mass constant.

*Digital/analogue interface (10 bit recommended), PC, Mechanics/smart pulley, 2 sets of slotted masses, Length of thick cotton, G clamp Top*11. Free Fall

The size of air resistance on falling objects is related to their size and speed. The effect of air resistance is related to the object's mass. The conditions are established where air resistance can be ignored. A stroboscopic picture of a falling golf ball is analysed and its speed versus time graph drawn. The acceleration of the ball is determined and related to the strength of gravity. Then the fun starts! Students are challenged to grab a bank note before it drops out from between their fingers. Grab it and its yours is the challenge. After everyone fails, the time for the note to drop out of reach is calculated. Then, reaction time of students is measured using a timer. This is found to be about twice the time of the calculation.

*Electronic timer with start and stop inputs. The timer must start when the two leads connected to the start input terminals are touched and stop when the two leads connected to the stop input terminals are touched. Top*12. Terminal Velocity

In this experiment students investigate the relationships between terminal velcoity, mass and surface area. A mechanics/smart pulley is clamped near the ceiling. A long cotton is passed over the pulley and a 50 g slotted mass tied to each end. The masses hang half way betwen the floor and the ceiling. A piece of A3 paper is attached to one of the masses. When they are released the paper falls smoothly and reaches terminal velocity which is measured by the PC. Adding sheets of paper varies the mass and keeps the area constant. Starting with a large sheet of paper and then folding the sides in varies the area and keeps the mass constant.

*Digital/analogue interface (10 bit recommended), PC, Mechanics/smart pulley, 2 sets of slotted masses, Length of thick cotton, A3 paper, Large sheet of paper, G clamp Top*13. Sky Diving

Data is given about the vertical distance fallen by a skydiver during the first 20 sec of free fall. Students analyse the data and calculate the speed and acceleration of the diver. They then determine the resultant force on the sky diver and then calculate the magnitude of the air resistance acting on the diver. They then determine the relationship betwen the magnitude of the air resistance and the speed of the diver. This exercise is best done using a spreadsheet.

*No equipment needed Top*14. Projectile Motion

Students analyse the vertical and horizontal motion of a multi flash photo of a projectile. The equation is discovered that calculates the range of a projectile in terms of its initial velocity and angle of launch. The difference in the range when a projectile is thrown at various places around the earth is investigated.

*Compass, ruler and a set square Top*15. CircularI Motion

Students use an electric motor mounted on an arm that is attached to a stand. The motor whirls a rubber ball in a circle. By measuring the mass of the ball, the frequency the ball and the heights above the desk of the motor and the ball as it moves, students can determine the relationship between centripetal force and frequency. Three balls with differing mass and three different length connecting lines enable the relationships between centripetal force, radius and mass to be found. The circular motion kit is available from IEC (Australia).

*IEC Circular Motion Kit (available from IEC Australia), Retort stand and bosshead, 2-12 V DC power supply, Rheostat, Stop watch and 1 meter ruler*Top16. CircularII Motion

Students use a mechanics pulley and an accelerometer attached to an interface to log data as the accelerometer rotates on a phonograph turntable (belt removed so it turns freely). This clever arrangement of the equipment enables the results needed to determine the relationship between centripetal acceleration and velocity to be gathered on 15 sec. Analysis is done after exporting the data to a spreadsheet. Changing the position of the accelerometer on the turntable enables the relationship between acceleration and radius to be found very quickly.

*Phonograph turntable, acceleration sensor, Mechanics/smart pulley, Stand and bosshead, interface, PC, G clamp*Top17. Motion in a Vertical Circle

In this fun experiment, students calculate the longest period of a bucket of water whirled in a vertical circle that causes the water to just stay in the bucket as it passes overhead. They verify the accuracy of the prediction with a small plastic bucket half full with water.

*Plastic bucket, 1 meter ruler, Stop watch Top*18. Friction

In this experiment, the relationship between static friction and the normal reaction is investigated. The coefficient of static friction is defined. They discover that the magnitude of the friction is independent of the area of contact.

*Friction block described in experiment, 0-5 N Force Measurer and 500 g of slotted masses, Inclined plane Top*19. Turning Corners

In this exercise, students analyse the forces acting on a car and the torques they create when turning corners both flat and banked. They discover what causes a car roll over. Students then investigate how an object at an ustable angle can be prevented from falling over if its base is accelerated. This leads to why a person on a bicycle needs to lean over when rounding a corner.

*Three 'Scalextric' banked curves, Glass marbles or steel balls, Stop watch and 30 cm ruler Top*20. Simple Harmonic Motion

In this experiment, students undertake vector analysis of the horizontal components of the centripetal force acting on an object moving with uniform circular motion. The relationship between horizontal force and displacement is established and SHM defined and the equation to calculate the period is developed. The theory is tested using a mass oscillating on the end of a spring. Students then use the same experimental set up as in 'Energy stored in a Spring' to plot the displacement, velocity and acceleration versus time graphs on a PC as the mass oscillates.

*Steel spring with a low stiffness with the turns not touching, Cotton, Stand, 2 Bossheads and clamps, 1 meter ruler, Mechanics/smart pulley, 2 sets slotted masses, Interface, PC Top*Top

21. Universal Gravitation

In this exercise the equation that calculates the gravitational force between two masses is developed and tested using data of the motion of the planets. It is used to determine the theoretical value of the gravitational field strength of the earth at its surface. Students learn to use the inverse square law to determine the strength of the earth's field at the distance of an orbiting satellite.

*No equipment needed Top*22. Motion of the Moon and Planets

In this exercise students analyse data about the motion of the planets to discover Kepler's three laws. They investigate the consequence of the non-constant speed of the earth in its orbit - the variation in the length of the day. The centre of mass of the Earth/Moon system is investigated. Students investigate the motion of the two bodies relative to their centre of mass and discover the centripetal force acting towards the centre of mass is the same for each.

*30 cm ruler Top*23. Satellites

Students investigate the conditions needed for a satellite to be set up in a stable orbit. The radius and period of a satellite in geosynchronous orbit is determined. The energy need to get a satellite into a geosynchronous orbit is estimated.

*30 cm ruler Top*24. Feeling Weightless and Tides

Students investigate how objects can be made to appear weightless when in a non-zero gravity environment. They then discover why objects floating in a space shuttle slowly drift apart. This situation is likened to the water on either side of the earth and why tides occur is explained. Students use their new knowledge to determine that the moon has about twice the tidal influence as the sun.

*No equipment needed Top*25. Force and Time

In this experiment, students are introduced to the concepts of impulse and momentum. Using light gates and a glider sliding down a sloping air track, it is proved that the impuse given to the glider by gravity is equal to its change in momentum.

*Air track, 3 light gates, 2 timers, glider with foam flag, 1 meter ruler Top*26. Collisions in 1-D

Students analyse the strobscopic pictures of the collisions between gliders on an air track. They discover the conservation of momentum, that each glider received the same sized impulse and the same sized force.

*Air track, one large and one small glider, 4 magnets, 2 stems with white cylinders, Needle and blu-tack or plasticene Top*27. Newton's Cradle

Students analyse the ball's on the 'executive toy' called Newton's cradle. They discover that conservation of momentum does not explain what is observed - another factor must be at work. They are introduced to the concept of kinetic energy.

*Newton's cradle Top*28. Force and Distance

In this experiment the students are introduced to the concept of work and shown that it is related to kinetic energy. Using light gates and a glider sliding down a sloping air track, it is proved that the work done on the glider by gravity, is equal to its change in kinetic energy.

*Air track, 3 light gates, 2 timers, glider with foam flag, 1 meter ruler Top*29. Collisions in 2-D

Students study the momentum and kinetic energy of two steel balls before and after a collision. One ball is suspended and another rolls down a ramp. After collision they fall to the floor and from where thy land, horizontal components of velocities are determined.

*Collision in 2 - D kit, Masonite board, Large piece of white paper, 2 sheets of carbon paper, Ruler and set square Top*30. Elastic and Inelastic Collisions

Students analyse the data given about elastic and inelastic collisions. Students investigate the momentum and kinetic energy before, during and after the two collisions. The concept of stored energy is introduced.

*No equipment needed Top*31. Centre of Mass

Students analyse a multi-flash photo of a collision between two air table pucks. Students determine the position of the centre of mass and discover it moves with constant velocity even though the pucks collided. The students calculate the velocity of each puck relative to the centre of mass and discover that the total momentum is zero in the centre of mass frame of reference.

*Compass, 30 cm ruler and a set square Top*32. Energy Transfer

Students use a light gate and a PC to measure the speed of a pendulum bob at the bottom of its swing. They calculate the bob's kinetic energy at the bottom and compare it to the calculation of the bob's gravitational potential energy at release.

*Pendulum bob, Cotton, Stand, Bosshead and clamp, Light gate, interface, PC, 30 cm ruler Top*33. Elastic Potential Energy in Springs

Students use a mechanics/smart pulley connected to an interface to log data when a mass oscillates on the end of a spring. After transferring the data to a spreadsheet, the kinetic energy and changes in elastic and gravitational potential energies are calculated as the mass drops from the top to the bottom of its motion. The total energy of the system is plotted against time. No more letting the mass drop and guessing its position when it stops. The ingenious arrangement of the equipment is very simple and very effective.

*Low stiffness steel spring with the turns not touching, Cotton, Stand, 2 Bossheads and clamps, 1 meter ruler, Mechanics/smart pulley, 2 sets slotted masses, Interface, PC Top*34. Power Transfer in Exercise

In this experiment, students estimate how powerful they are when they do step ups, push ups and climb stairs.

*Bathroom scales, Tape measure, 1 meter ruler, Stop watch Top*]