4-FAD-01

Outcomes

• Pupils can arrange all the GCSE quantities into two groups: scalars and vectors.
• Pupils appreciate that force is a vector quantity and understand the nature of this.
• Pupils can name and label forces on stationary objects using arrows (1-D) and show that they are balanced.
• Pupils can add force vectors that act along a line.

Specification References

• 1.10 distinguish between vector and scalar quantities
• 1.11 appreciate the vector nature of a force
• 1.12 add forces that act along a line

Starter

• Introducing the idea of vectors to the class. Here are two options.
• 1) Hide a £1 coin a set distance from a pre-determined place in the classroom. Stand on this spot with a stop watch. Choose two students and tell them "There is a £1 coin 2 meters from my current position. If you can find it within 6 seconds it's yours!" Stop the students after the 6 seconds. Encourage the students to discuss your statement. Is there enough information included in the statement to find the £1 coin? The displacement required to find the coin has not been fully described. Now, tell them " There is a £1 coin 2 meters and directly North of my current position, start the stop watch again. They will hopefully find the coin this time. You could even tape it to the ceiling if you wish! This statement now provides a complete description of the displacement vector - it lists both magnitude (2 meters) and direction (North) relative to a reference or starting position. Vector quantities are not fully described unless both magnitude and direction are listed.
• 2) Ask the pupils to estimate the number of steps you need to take to reach the back of the classroom. Once you have an agreed number of steps from the class begin walking to the back of the room (counting the number of steps as you go along) but walk in and out of the desks. Question how the pupils could have gotten it so wrong and begin to introduce the terms distance and displacement and how vector quantities are not fully described unless both magnitude and direction are given.
• Next, split the class into groups of six and give each group a pack of cards which contain all the GCSE quantities. Ask them to divide them into two groups: 1) those that have a direction and can be represented with an arrow (a vector) and 2) those that do not (a scalar).
• These cards should be left while they carry out work on the force table.

Main Body of Lesson

• The groups of six can be split into groups of two to investigate vectors on the force tables. They can work through this Force Table Worksheet where they are asked to apply different arrangements of masses/forces pulling on a central block. They are asked to make and record a prediction before releasing the block and also to record their observations.
• Regroup them and ask them to discuss their observations and write their own definition for a vector and scalar quantity on the mini whiteboards.
• Discuss the groups outcomes and write definitions for vectors and scalars to be recorded in their books. Emphasise that vector quantities could be negative whereas scalar quantities cannot. (They may argue about temperature where they can be introduced to the Kelvin scale)
• The groups will reassess their vector and scalar groups after the powerpoint.
• Use this Vectors Powerpoint which include the definition for vector and scalar quantities and goes through the remainder of the lesson.
• Discuss the images and have the class help label the forces using arrows. Guide them towards the correct direction of arrow and type of force as revision from the 3rd year. Begin looking for pairs of forces which are balanced and result in zero force on the object.
• Explain that force vectors are depicted as arrows to show the direction, with the length of the arrow representing the magnitude of the force. You could introduce the 'head' and 'tail' of the force vector.
• Also introduce the idea that the resultant of two given forces is an imaginary force and is equivalent to the actual forces. It would have the same effect as the real forces combined.
• Go through the examples on how to add vectors from the power point slide. Emphasis how to add vectors 'head to tail'. Make them redraw the arrows in 'head to tail' formation.
• The powerpoint does go into perpendicular vectors, with some real life examples (this is a bit beyond the syllabus and can be skipped over if there is little time or the group is struggling with vectors in 1-D.
• REGROUP - Have the groups reassess their vector and scalar groups from the beginning of the lesson and make any corrections they feel they need to make.
• Make a centralised list on the board and have them copy this under their definitions in their books.

Plenary

• Vector Addition Game Print A3 sheet from Science shared in FAD-01 folder
• Supply the pupils with large squared paper with the same starting point/'Home Base' and end point/ 'Base One' labelled.
• Following the two rules they are to draw a route from the Home Base to Base One. Emphasise that they are not to hugely complicate the journey. Don't forget to put arrows on each section of your journey.
• Rule 1 - They can only move vertically or horizontally.
• Rule 2 - Each section must be a whole number of squares.
• Invite six to eight pupils to come to the front of the class with their journeys (It would be better to select a group with a range of journey distances). Tell the class that you will be asking them to add the vectors up and can they order the pupils from largest vector displacement to smallest vector displacement.
• Ask them to now add all their horizontal and vertical vectors being sure to pay attention to their direction. Ask them to write their answers on the white boards in the form of (x,y). When they are all finished ask them to hold the whiteboards up together. Why are they the same?
• Ask them to now draw the shortest possible route in a different colour pen. Remind them of the rules! What do they notice?
• Ask them to now draw another route, in another colour, 'as the crow flies', obviously ignoring the rules.
• Emphasis that the three sets of vectors all result in the same displacement. If there is time and the class is able enough you could ask them to find the hypotenuse from sum of the squares of the two smaller sides which they could go onto measuring and verifying.

Homework

• Use this Vector Homework sheet. Student add forces along a line and may go onto an extension activity where they both label and add up forces for a number of situations.
• Students could also research the difference between speed and velocity and how the change in velocity can occur by the velocity only changing direction and not magnitude. This could lead them to the idea of circular motion.

Additional Information

EXTENSION - If there is time and you wish to extend to 2-D vectors a nice activity is to use the trio of ropes tied to a loop. In groups of four, have three pupils pull on the three ropes using forcemeters. They should pull and create a 'balanced loop' which is resting on the A3 paper. The fourth member uses a ruler to trace the three ropes with a pencil (on both sides) and label the force from the forcemeter. The centre of the loop should also be marked. Now have them take the loop and rope away and using the pencil draw the force vectors leading from the centre of the loop. The vectors should be in the correct direction and be drawn to scale. (i.e 2cm = 1N) Now using the acetate sheet they should trace the vectors one at a time 'adding them' head to tail. (They will get the direction correct if they concentrate on keeping the same acetate edge parallel with the same paper edge. The three force vectors should create a triangle showing that they are balanced or the resultant is zero.

Resources Required

• Class set of quantity cards in envelopes + whiteboards
• Class set of mini whiteboards
• Force tables - boards x 12, bull dog clips with one lever bent upward x 48, string, block with four eyelets at the centre of each side, 100g mass sets, deep plastic trays x 24

• Class set of large A3 sheets of squared paper(large squares)with the same 'Home Base' and 'Base One' labelled.
• Extension activity only - Set of 'ring with three ropes' systems, 3 Newton meters x 3, A3 sheet x 1, acetate sheet x 1 , rulers x 1 and OHP pen x 1.

Textbook References

• None

Website References

• None

Safety/Hazards

• None

Notes

• None