Presentation on theme: "Vectors vs. Scalars Pop Quiz: Which of these do you think are vector quantities? Mass, Temperature, Distance, Displacement, Speed, Velocity, Acceleration,"— Presentation transcript:
Vectors vs. Scalars Pop Quiz: Which of these do you think are vector quantities? Mass, Temperature, Distance, Displacement, Speed, Velocity, Acceleration, Force, Work, Energy, Power, Momentum, Time
A vector is an arrowed line. A vector has a tail and a head. The head points in the direction of the vector. The length represents the size (magnitude) of the vector.
Represent these displacements as vectors on your book Use scale 1:100 (i.e. 1cm on your book is equivalent to 1m in real) 1.Jimmy travels 13 m west. 2.Bobby travels 3 m south. 3.Timmy travels 6 m, 45 o north of east. 4.Libby travels 5 m, 80 o north of west.
The bearing of A from B is 065 o. The bearing of B from A is 245 o.
Vector Addition Vector A = 7 m towards east Vector B = 4 m towards north Vector A + B = ???
Adding Vectors (to find the resultant vector) Q1. A car travels 3 km east, then 4 km south. Find the car’s total displacement by drawing a scaled vector diagram. Q2. During a tug-of-war, the rope is pulled with a force of 250 N towards left and a force of 300 N towards right. Find the resultant force acting on the rope.
Negative Vector Vector A = 7 m towards east Question: What would be the negative vector A? Answer: 7 m towards west
Vector Subtraction Vector subtraction is the same as the vector addition, only adding a negative vector. A – B = A + - B Vector A = 7 m towards east Vector B = 4 m towards north Vector A – B = ???
Vector Subtraction (to find the change, Δ = f – i ) Q1. A car initially travelling at 15 ms -1 east turns a 90 o corner and ends up travelling at 10 ms -1 north. Determine the change in velocity by using a vector diagram. Q2. A ball initially travelling towards a batman at 5 ms -1 collides with him and rebounds at 4 ms -1 in the opposite direction. Find the ball’s change in velocity.
Do all questions from Activity 8A (green textbook, pg. 98) except for Q9.
Do now Vector A = 4 cm east Vector B = 4 cm north Vector C = 6 cm west Vector D = 5 cm bearing 45 O Draw vector diagrams to show: 1. A + B5. A – B 2. C + D6. A – D 3. A + B + C7. A – C 4. A + C8. D – B
Components of a Vector Any vector can be broken down into two components – Horizontal and Vertical Any vector can be drawn as the sum of two other vectors drawn at right angles to each other. The two vectors are called components of the first vector.
Vector A = 4 cm north Vector B = 3 cm east Vector C = 5 cm bearing 37 o Draw a vector diagram to show that: A + B = C Vector A is the vertical component of Vector C Vector B is the horizontal component of Vector C