Jan throws a ball into the air and catches it on its way down Jan throws a ball into the air and catches it on its way down. Think about the ball at point A, on its way up to the highest point B How would you describe the motion of the ball at point A? Getting faster, moving at a steady speed, slowing down? Which of these diagrams best shows the vertical forces on the ball at A? B A The only force is the upward one from Jan’s throw The only force is gravity There are 2 forces: gravity and air resistance There are 3 forces: gravity, air resistance and the force of the throw None of these, the forces are…. 1 2 3 4 5

Some classic Physics misconceptions or ‘common sense’ conceptions Heavier objects fall faster than light ones If there is motion there is a force acting. The force is in the direction of motion If there is no motion, then there is no force acting A moving object has force within it which keeps it going Passive objects, like a table or wall don’t exert a force

Vectors & Scalars I can identify vectors and scalars I can add and resolve vectors I have started to apply a structured problem solving strategy to tackle physics problems

A Scalar is any physical quantity that is not directional A Vector is any physical quantity that has a direction as well as magnitude Eg. you know that forces are represented by arrows with a given length and direction

Scalar or Vector? density temperature length acceleration energy mass weight volume force velocity displacement

Displacement … is the distance and direction (as the crow flies) that you have been displaced from your origin. For example, Google maps says you would have to walk 750m from school to Green Park shops, but your displacement would be about 500m south east.

Displacement What is the resultant displacement in these two examples? If you walked all the way around Willen Lake what would your displacement be?

Adding Vectors What will be the Resultant force on these two blocks? Vector Diagram 6.0 + 8.0 = 14.0 N to the right 6.0 N 8.0 N 8.0 - 6.0 = 2.0 N to the right

Crossing the river How would your swimming velocity and the current velocity combine?

Simple vector problems D A B C A +B A – B A + 2B C + D C – D 2C – 2D 10

How can we find the resultant of these two forces? What direction will the force take roughly? How big will the force be, relative to force 1 and force 2? Rearrange your diagram to produce a vector diagram Force 1 = 10.0N What techniques can you use to find the exact magnitude and direction of the resultant force? Use a ruler and protractor to produce an accurate scaled drawing Pythagoras and Trigonometry, for vectors at right angles to each other Force 2 = 7.0N

Predict the Resultant… This activity can be done by measuring the velocities of the support trollies and the bridge trolley. The ink trail provides the resultant addition vector. Its angle and length will depend on the relative component velocities. How will the ink trail change if the bridge trolley travels faster or slower than the supporting trolleys? How might the trail change if the bridge was sloped so that the trolley had constant acceleration?

What will be the combined effect of these two forces? Draw a scale diagram to find the solution

None right-angled triangles C 40 b 6 140 5 B A c Cosine Rule: C2 = 62 + 52 – 60 cos140 = 10.34N Cosine Rule: C2 = a2 + b2 – 2ab cosC Sine rule: sinB = sin140 5 10.34 sinB = 5 sin140 10.34 Sine rule: sinB = sinC b c =18.11o below a

?N ?N More or less than 12N? 12N 12N

What is the reaction, or normal force of the slope on the block?

Resolving vectors into two perpendicular components Physicists may need to know the effect that a single force (or other vector) has in two other directions What would you estimate the size of this force is vertically and horizontally ? Which will be bigger, the vertical or the horizontal component? 5.0N ? 40o ? How can we calculate them ?

Resolving Vectors SohCahToa Cosine 40 = adj/hyp Cos 40 = h/5 h = 5 Cos 40 h = 3.8N Sine 40 = opp/hyp Sine 40 = v/5 v = 5 Sin 40 v = 3.2N CHECK! Are these proportions about right? And, using Pythagorus, 52 = h2 + v2 40o So, a force sharing to the known angle, has magnitude FcosѲ The force opposite the known angle has magnitude FsinѲ This is true for other vectors v Hypotenuse = 5N FsinѲ 3.2N 40o h FcosѲ 3.8N

Question 1 You are walking at 4.0 m s–1 in a direction 30° N of E. What is the component of your velocity in an easterly direction? 3.46 m s–1 This is the same answer as you found by scale drawing, but without the uncertainties introduced by drawing. Take care not to be misled by the apparent accuracy of this answer. (The calculator gave 3.464 1016... m s–1.) If your speed is given as 4.0 m s–1, you can only give the value of the component to two significant figures. Question 2 A train is gradually travelling up a long gradient. The speed of the train is 20 m s–1 and the slope makes an angle of 2° with the horizontal. The summit is 200 m above the starting level. How long will it take to reach the summit? From the diagram in the question, it is clear that sin2° = 200 / slope, so that the length of the slope is: Then the time taken is:

Question 3 You set off to run across as empty supermarket parking strip, 100 m wide. You set off at 55° to the verge, heading towards the entrance to the supermarket. Your speed is 8 m s–1. How long will it take you to reach the far entrance? How far along the opposite side of the parking strip you will arrive? 15.3s 70.2m

Question 4. Flying in a side wind Relative velocities and displacement In these questions, you have to find the velocity and the displacement of a bird relative to the ground, when it is actually flying relative to the wind. A bird flies at a steady speed of 3 m s–1 through the air. It is pointing in the direction due north. However, there is a wind blowing from west to east at a speed of 2 m s–1. 1.What is the velocity of the bird relative to the ground? 2.What is the displacement of the bird, relative to its starting point, after it has flown for 20 seconds? 3.In what direction should the bird point if it is to travel in a northerly direction? Hints 1.Velocity is a vector, and has both magnitude and direction. 2.How is velocity defined in terms of displacement? 3.To fly due north requires the bird not to move in an easterly direction. What must the east–west component of its velocity be?

2. After 20 s, the displacement of the bird is found from displacement = velocity ´ time. The direction of displacement is as for velocity if the velocity is constant. The magnitude of the displacement is simply 3.6 m s–1 ´ 20 s = 72 m. 3. To fly due north, the bird has to fly in such a direction that it has a component of its velocity that cancels out the velocity of the wind. This means that it has to have a component of velocity equal to 2 m s–1 west. The diagram shows how this is done.

Adding Vectors How can we add together two vectors? B How can we find the magnitude and direction of the displacement vector A-C? C A