Question 3 A car of mass 800kg is capable of reaching a speed of 20m/s from rest in 36s. Work out the force needed to produce this acceleration. m = 800kg v = 20 m/s u = 0 m/s t = 36s Equations: F = ma a = (v-u)/t a = (20 – 0) / 36 = 0.56 m/s2 F = 800 x 0.56 = 444.44N

Question 3 b. What is the weight of the car? Mass = 800kg Equation: W = mg W = 800 x 10 = 8000N c. Work out the ratio of the car’s accelerating force to its weight. Ratio = 444.44 / 8000 = 0.056

Question 4 The engines of a ship have broken down. The ship is being towed into port by a tugboat at a steady speed of 4.0m/s. The towing cable pulls the ship with a force of 22500N. The ship experiences a drag force due to the water. This force opposed the motion of the ship. What is the size of the drag force? Constant speed therefore no resultant force Drag force = towing force = 22500 N

Question 4 b. The total mass of the ship is 8.0 x 106 kg. When the cable is released, estimate how long the ship takes to stop assuming the drag force does not change. Now resultant force slowing ship = drag force. Equation: F = ma rearranging a = F/m a = 22500 / 8.0 x 106 = 2.81 x 10-3 m/s2 a = (v-u)/t rearranging t = (v-u)/a t = (0-4)/-2.81 x 10 -3 = 1422.22 s = 23 mins

Calculate the Resultant Force in each case… Extension: Calculate the acceleration if the planes mass is 4500kg. C) B) 1.2 X 103 Thrust A) 1.2 X 103 Thrust 1.2 X 103 Thrust 5.0 X 104 Lift 0.8 X 103 Side-wind 0.2 X 103 Drag 1.2 X 103 Drag 4.5 X 104 Weight 0.2 X 103 Drag

Learning Objectives By the end of this lesson you should be able to... Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another.

Quantities A scalar is a quantity that has size (number) only. Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Quantities A scalar is a quantity that has size (number) only. A vector has both size and direction.

Scalar Vector Power Acceleration Distance Mass Displacement Energy Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Scalar Vector Power Acceleration Distance Mass Displacement Energy Speed Current Force Velocity Momentum Time

Scalar Vector Power Distance Mass Energy Speed Acceleration Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Scalar Vector Power Distance Mass Energy Speed Acceleration Displacement Current Force Velocity Momentum Time?

Adding Parallel Vectors Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Adding Parallel Vectors 6N 12N 1N The result of combining vectors is called the resultant (or net) If the vectors are pointing in the same direction they add up. If the vectors are pointing in opposite directions they subtract.

Vectors at right angles Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Vectors at right angles Now consider this situation. Note that the vectors do not have to be force, they can be velocity or any other vector quantity Air craft velocity 30 m/s Due North. Wind velocity 10 m/s West

Vectors at right angles Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Vectors at right angles What happens? The aircraft will be blown off course. Actual direction of travel Air craft velocity 30 m/s Due North. Wind velocity 10 m/s West

Vectors at right angles Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Vectors at right angles A scaled diagram will allow you to solve both the length of the actual journey and the direction but it is time consuming. Actual direction of travel Air craft velocity 30 m/s Due North. Wind velocity 10 m/s West

Vectors at right angles Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Vectors at right angles By re-arranging the arrows (components) we can use Pythagoras theory to find the answer. Actual direction of travel Air craft velocity 30 m/s Due North. Wind velocity 10 m/s West

Vectors at right angles Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Vectors at right angles By re-arranging the arrows we can use Pythagoras theory to find the answer. Actual direction of travel a2 = b2 + c2 A2 = 302 + 102 A = 31.6 m/s Air craft velocity 30 m/s Due North. Wind velocity 10 m/s West

Vectors at right angles Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Vectors at right angles The value for the hypotenuse is the magnitude but as these are vectors we also need the direction. We can use trigonometry for this final step. a2 = b2 + c2 A2 = 302 + 102 A2 = 31.6 m/s Actual direction of travel Air craft velocity 30 m/s Due North. Wind velocity 10 m/s West

Vectors at right angles Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Vectors at right angles This provides us with the magnitude but as these are vectors we also need the direction. We can use trigonometry for this final step. SOH CAH TOA Identify the 3 sides and label O, H, A. Find the angle you are looking for. 3. Solve Actual direction of travel 31.6 m/s Air craft velocity 30 m/s Due North. H O Wind velocity 10 m/s West A

Vectors at right angles Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Vectors at right angles This provides us with the magnitude but as these are vectors we also need the direction. We can use trigonometry for this final step. SOH CAH TOA Cosθ = A / H Cosθ = 10 / 31.6 Cosθ = 0.316 θ = Cos-1 (0.316) θ = 71.5 Actual direction of travel 31.6 m/s Air craft velocity 30 m/s Due North. H O A Wind velocity 10 m/s West

Worked Example #2 40m 120m First step: Use Pythagoras’ theorem Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Worked Example #2 40m 120m First step: Use Pythagoras’ theorem a2 + b2 = c2 1202 + 402 = c2 C2 = √1202 + 402 C = 126.49

SOH CAH TOA H O ∂ A 40m 120m Second step – Use trig Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. SOH CAH TOA H O 40m ∂ 120m A Second step – Use trig Identify 3 sides and label O, H, A Find the angle you are looking for

SOH CAH TOA H O ∂ A 40m 120m Second step – Use trig Sin∂ = O / H Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. SOH CAH TOA H O 40m ∂ 120m A Second step – Use trig Sin∂ = O / H Sin∂ = 40 / 126.48 Sin∂ = 0.3 ∂ = Sin-1 (0.316) ∂ = 18.43°

Two for you to try… 10km 10km 210m 200m 100ms-1 5ms-1 Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Two for you to try… 10km 10km 210m 200m 14.1 km and 100.1m/s 100ms-1 5ms-1

Further Q’s A car travels 50 km N and then returns 30 km S. The whole journey takes 2 hours. Calculate: The distance travelled. The displacement. The average speed The average velocity. An aircraft pilot wishes to fly north at 800 km/h. A wind is blowing at 80 km/h from the west. What speed and course must he select to fly the desired course?

Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Finding Components We can use the same process in reverse to work out the vertical and horizontal component forces when given the vector. This 24 N force is acting at an angle of 35 degrees to the horizontal. Some of it effectively acts vertically and some horizontally.

We can use sine and cosine to work out components of the force Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. We can use sine and cosine to work out components of the force

Example A boat sails at 10 km/h on a bearing of 040. Calculate: Learning Objectives By the end of this lesson you should… Explain the difference between the terms scalar and vector List the quantities which are described as either scalar or vectors. Calculate the resultant force when multiple forces act in parallel and perpendicular to one another. Example A boat sails at 10 km/h on a bearing of 040. Calculate: Its velocity due North Its velocity due East The distance travelled in 3h. The displacement North and East from where it started.

Vectors multiple choice. Assume each square is 20m x20m If a person walks from D to H to G to C, then the distance walked is _____ m a. 128m b. 180m c.213m d.460m e. 480m F. 533m g. 620m h none of these, If a person walks from D to H to G to C, the magnitude of the displacement is ___m A 128m, b 180m, c 401m d 460m, e 480m, f 533m, g 620m, h None of these.

Vectors Multiple choice Now calculate the direction of the displacement in a counter clockwise direction from East. If the path is now H, E, C, G calculate A. The distance travelled B. The displacement from the initial position C. the direction of displacement counter clockwise from East

Questions (Complete Physics P47) 1. Define scalar and vector quantities 2. There are two forces acting on a body 5N and 12 N a What is the magnitude of the greatest resultant force b. What is the magnitude of the minimum resultant force C. If the forces are perpendicular what is the magnitude and direction of the resultant force?

Questions (Complete Physics p47) 3. A lawn mower is pushed by a force of 100N at 30o from the horizontal . Calculate A. The horizontal and vertical components of the force B the total downward force if the weight of the lawnmower is 300N C. If the lawnmower is pulled what will happen to the magnitude of the downward force.