Chap 4:Dynamics: Newton’s Law of Motion No Homework next week

Solving Problems Involving Projectile Motion Example 3-7: A kicked football. A football is kicked at an angle θ0 = 37.0° with a velocity of 20.0 m/s, as shown. Calculate (a) the maximum height, (b) the time of travel before the football hits the ground, (c) how far away it hits the ground, (d) the velocity vector at the maximum height, and (e) the acceleration vector at maximum height. Assume the ball leaves the foot at ground level, and ignore air resistance and rotation of the ball.

Relative velocity Reference Frames y bug car vCA vBA x Earth=A=stationary reference frame vBA=velocity of the bug, B, relative to the earth , A vCA= velocity of the lemon car, C, relative to the earth, A

Relative velocity car y C A B bug vCA vBA x Earth=A=stationary reference frame We can add reference frames to the bug, B and to the Lemon car, C vBA=velocity of the bug, B, relative to the earth , A VCA=-VAC vBC=vBA-vCA Or vBC=vBA+vAC Notice how the outer subscripts on the right side of the equation correspond with those on the left, and how the inner subscripts are the same but do not exist on the left. Think of them as canceling.

Relative Velocity Here, vWS is the velocity of the water in the shore frame, vBS is the velocity of the boat in the shore frame, and vBW is the velocity of the boat in the water frame. The relationship between the three velocities is:

Relative Velocity Example 3-14: Heading upstream. A boat’s speed in still water is vBW = 1.85 m/s. If the boat is to travel directly across a river whose current has speed vWS = 1.20 m/s, at what upstream angle must the boat head?

Defining Force Two kinds of forces: Force = Units: A push or a pull Newtons = kg.m/s2 Long range: Contact: Gravitational force Electromagnetic force Everything else Whenever two objects touch

Measuring Force We can use a calibrated spring scale to measure force Force is a vector! Net Force = the vector sum of all forces acting on an object

Ah, but force is a vector. Images: http://library.thinkquest.org/25844/dynamics/images/ski.gif; http://www.mwit.ac.th/~physicslab/applet_04/physics_classroom/Class/vectors/u3l3b

Kinds of forces and direction Gravitational Force: (W) or Fg attraction between earth and an object. Forces on the Most Common Contact Forces: Friction: (f) parallel to contact surface N Normal: (N) Perpendicular to contact surface T f Tension: (T) along rope or cord or… W

Newton’s First Law of Motion This is Newton’s first law, which is often called the law of inertia: Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. Figure 4-3. Caption: F represents the force applied by the person and Ffr represents the force of friction.

Newton’s First Law of Motion Inertial reference frames: Newton’s first law does not hold in every reference frame, such as a reference frame that is accelerating or rotating. An inertial reference frame is one in which Newton’s first law is valid. This excludes rotating and accelerating frames. How can we tell if we are in an inertial reference frame? By checking to see if Newton’s first law holds!

Mass Mass is the measure of inertia of an object; mass is a measure of an object’s resistance to change its velocity. In the SI system, mass is measured in kilograms. Mass is not weight. Mass is a property of an object. Weight is the force exerted on that object by gravity. If you go to the Moon, whose gravitational acceleration is about 1/6 g, you will weigh much less. Your mass, however, will be the same.

Equilibrium When the net force acting on an object is zero, then it is in equilibrium. and and An object in motion remains in motion And An object at rest remains at rest if the net external force acting on the object is zero. a=0, v=constant

Question A UFO is hovering, stationary, 2000m above the earth. The net force on the UFO is 1) zero 2) due east 3) upwards 4) downwards

Question An airplane is flying due East at a constant velocity of 590 mph. The net force on the airplane is 1) zero 2) due east 3) upwards 4) downwards

Question The Earth travels around the Sun with a constant speed. The net force on the Earth is zero nonzero

Question A skydiver is falling toward the Earth at terminal velocity, that is, at constant speed. The net force on the skydiver is zero nonzero

Newton’s Second Law of Motion Newton’s second law is the relation between acceleration and force. Acceleration is proportional to force and inversely proportional to mass. It takes a force to change either the direction or the speed of an object. More force means more acceleration; the same force exerted on a more massive object will yield less acceleration. Figure 4-5. Caption: The bobsled accelerates because the team exerts a force.

Newton’s Second Law of Motion Force is a vector, so is true along each coordinate axis. The unit of force in the SI system is the newton (N). Note that the pound is a unit of force, not of mass, and can therefore be equated to Newtons but not to kilograms.

Newton’s Second Law of Motion Example 4-2: Force to accelerate a fast car. Estimate the net force needed to accelerate (a) a 1000-kg car at ½ g; (b) a 200-g apple at the same rate. Example 4-3: Force to stop a car. What average net force is required to bring a 1500-kg car to rest from a speed of 100 km/h within a distance of 55 m? Figure 4-6. 4-2. Use Newton’s second law: acceleration is about 5 m/s2, so F is about 5000 N for the car and 1 N for the apple. 4-3. First, find the acceleration (assumed constant) from the initial and final speeds and the stopping distance; a = -7.1 m/s2. Then use Newton’s second law: F = -1.1 x 104 N.