Today s Lecture: Kinematics in Two Dimensions (continued) A little bit of chapter 4: Forces and Newton s Laws of Motion (next time)

Transcription

1 Today s Lecture: Kinematics in Two Dimensions (continued) Relative Velocity - 2 Dimensions A little bit of chapter 4: Forces and Newton s Laws of Motion (next time) 27 September

2 Relative Velocity (2 Dimensions) Velocity of car A relative to car B is: v AB v AG v GB v AG v BG Magnitude: Direction: tan AB AG GB v v v m s September

3 Crossing a river (example 3.11): The engine of a boat drives it across a river that is 1800m wide. The velocity of the boat relative to the water is 4.0 m/s directed perpendicular to the current. The velocity of the water relative to the shore is 2.0 m/s. (a) What is the velocity of the boat relative to the shore? (b) How long does it take for the boat to cross the river?

4 Crossing a river (a) What is the velocity of the boat relative to the shore? v v v BS BW WS 2 2 BS BW WS v v v 4.0m s 2.0m s 4.5m s tan (b) How long does it take for the boat to cross the river? t 1800 m 450 s 4.0m s

5 Problem 3.53: A hot air balloon is moving relative to the ground at 6.0 m/s due east. A hawk flies at 2.0 m/s due north relative to the balloon. What is the velocity of the hawk relative to the ground? 27 September

6 Example falling rain (problem 3.70): A person looking out the window of a stationary train notices that raindrops are falling vertically down at a speed of 5.0 m/s relative to the ground. When the train moves at constant velocity, the raindrops make an angle of 25 as they move past the window. How fast is the train moving?

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8 Problem 3.56: Relative to the ground, a car has a velocity of 18.0 m/s, directed due north. Relative to this car, a truck has a velocity of 22.8 m/s, directed 52.1 degrees south of east. Find the magnitude and direction of the truck s velocity relative to the ground. 27 September

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10 Problem 3.57: A hockey player is skating due south at a speed of 7.0 m/s relative to the ground. A teammate passes the puck to him.the puck has speed of 11 m/s relative to the ground and is moving in a direction 22 degrees west of south. Find the magnitude (relative to the ground) and direction (relative to due south) of the puck s velocity as observed by the hockey player. SUBTRACTION RULE: v The resultant vector head HG Always points toward the v PG head of the vector that is being subtracted from. v PH v PG v GH v PG v HG 27 September

11 Problem 3.69: An aircraft is headed due south with a speed of 57.8 m/s relative to still air. Then, for 900 s a wind blows the plane so that it moves in a direction 45 degrees west of south, even though the plane continues to point due south. The plane travels 81 km with respect to the ground in this time. Determine the velocity of the wind with respect to the ground. 27 September

12 Chapter 4 Forces and Newton s Laws of Motion

13 Chapter 4: Forces and Newton s Laws Force, mass and Newton s three laws of motion Newton s law of gravity Normal, friction and tension forces Apparent weight, free fall Equilibrium

14 Force and Mass Forces have a magnitude and direction forces are vectors Types of forces : Contact example, a bat hitting a ball Non-contact or action at a distance e.g. gravitational force Mass (two types): Inertial mass what is the acceleration when a force is applied? Gravitational mass what gravitational force acts on the mass? Inertial and gravitational masses are equal.

15 Arrows are used to represent forces. The length of the arrow is proportional to the magnitude of the force. 5 N 15 N Inertia is the natural tendency of an object to remain at rest or in motion at a constant speed along a straight line. The mass of an object is a quantitative measure of inertia. SI Unit of Mass: kilogram (kg) SI unit of force: Newton (N) 1N m s kg m kg 2 2 s

16 Newton s Laws of Motion 1. Velocity is constant if a zero net force acts 2. Acceleration is proportional to the net force and inversely proportional to mass: a 0 if F 0 F a so F m ma Force and acceleration are in the same direction 3. Action and reaction forces are equal in magnitude and opposite in direction

17 Newton s First Law (law of inertia) Object of mass m Acceleration a 0 if F 0 Velocity v constant The velocity is constant if a zero net force acts on the mass. That is, if a number of forces act on the mass and their vector sum is zero: F net F... 1 F2 0 So the acceleration is zero and the mass remains at rest or has constant velocity.

18 Individual Forces Net Force 4 N 10 N 6 N 3 N 5 N 37 4 N

19 Some Examples: Why does a falling object reach so called terminal velocity? The force due to gravity is acting down, accelerating the object toward the ground. The object also experiences the force due to friction with molecules in the air, which is a result of a complicated interplay between air pressure, wind speed and direction, and the shape as well as the speed of the object. If the object falls long enough, at some speed the frictional force will be equal and opposite to the force due to gravity. The forces exactly cancel producing a zero net force: And the velocity is constant: i.e. Terminal velocity!

20 Why do you have to keep your foot on the accelerator pedal, even if you want to go at a constant velocity? The weight of the car produces friction between the tires and the road and the car will slow down due to this friction unless you continue to accelerate.