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) 29 September 2009 1
Question the moving walkway (problem 3.50): A moving walkway (speed ramp) at an airport is a moving conveyor belt on which you can either stand or walk. It is intended to get you from place to place more quickly. Suppose a moving walkway is 120 m long. When you walk at a comfortable speed on the ground, you cover this distance in 86 s. When you walk on the moving walkway at this same comfortable speed, you cover this distance in 35 s. The speed of the moving walkway relative to the ground is: (a) 1.4 m/s (b) 2.0 m/s (c) 2.4 m/s (d) 3.4 m/s (e) 4.8 m/s
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: 115.8 tan 32.3 25.0 2 2 AB AG GB v v v 25 15.8 29.6 m s 2 2 29 September 2009 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?
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 2 2 14.0 tan 63 2.0 (b) How long does it take for the boat to cross the river? t 1800 m 450 s 4.0m s
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? 29 September 2009 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?
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. 29 September 2009 8
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 a 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: The resultant vector head Always points toward the v HG head v PG of the vector that is being subtracted from. v PH v PG v GH v PG v HG 29 September 2009 9
29 September 2009 10
Chapter 4 Forces and Newton s Laws of Motion
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
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.
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
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
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.