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Transcript
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. 15 N 5N 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: m 1N kg 2 s Newton (N) kg m 2 s Newton’s Laws of Motion 1. Velocity is constant if a zero net force acts a 0 if F 0 2. Acceleration is proportional to the net force and inversely proportional to mass: a F m so F 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) Accelerati on a 0 if F 0 Object of mass m 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: Fnet F1 F2 .... 0 So the acceleration is zero and the mass remains at rest or has constant velocity. Individual Forces 4N 10 N Net Force 6N 5N 3N 37 4N 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! 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. Newton’s First Law It was a revolutionary idea that objects continue to move if no force acts: – experience shows that a force is needed to keep objects moving (friction) – it was believed that some cosmic force keeps the planets moving in their orbits In the absence of friction, objects continue to move at constant velocity if net force is otherwise zero (Nothing is done to the object). If the net force, including the force due to friction, is zero, objects move at constant velocity (Something is pushing or pulling to offset the force due to friction). Newton’s First Law FN m A crate is at rest on the ground: v 0 and a 0 What forces act on the crate? w the weight: w mg According to Newton’s first law, there must be another force so the net force acting on the crate is zero. It is the normal force of the ground acting on the crate FN w 0 FN w FN so the crate remains at rest Inertial Reference Frame Can be defined anywhere: • right here It is a coordinate system, (x, y, z) y • in your car... x An inertial reference frame is one that is not accelerated (moves at constant velocity, including zero velocity). • the law of inertia (first law) applies in an inertial frame – objects at rest remain at rest if no net force acts on them. • law of inertia does not apply in an accelerated (non-inertial) frame. Example: Driving around a corner – velocity changes, force has to be applied to keep objects from moving – a non-inertial frame. Newton’s Second Law Says what happens if the net force acting on a mass is not zero. The mass accelerates: Acceleration, a Fnet Fnet = net force acting on the mass proportional to Introduce the mass: a Fnet m or Fnet ma m is the “inertial mass”, a measure of how difficult it is to accelerate an object. Newton’s Second Law m = 1850 kg A free-body diagram shows only the forces acting on the car Two people push a car against an opposing force of 560 N. One exerts 275 N, the other 395 N of force on the car. What is the net force acting on the car? What is the car’s acceleration? Problem: A catapult on an aircraft carrier accelerates a 13,300 kg plane from 0 to 56 m/s in 80 m. Find the net force acting on the plane. Fnet ma (acceleration along a straight line) What is a? v 2 v 02 2ax or 562 0 2a 80 so a 562 / 160 19 .6 m/s 2 Therefore Fnet (13,300 kg ) (19.6 m/s 2 ) 261,000 N The direction of force and acceleration vectors can be taken into account by using x and y components. F ma can be decomposed into Fx ma x Fy ma y Then solve the equations separately in each direction. Problem 4.11 What is the acceleration of the block in the horizontal direction? Work out the components of forces in the x-direction. x 59 N No friction 33 N Problem 4.88 A 75 kg water skier is pulled by a horizontal force of 520 N and has an acceleration of 2.4 m/s2. Assuming the resistive force from water and wind is constant, what force would be needed to pull the skier at constant velocity? Problem 4.4 A special gun is used to launch objects into orbit around the earth. It accelerates a 5 kg projectile to 4x103 m/s by applying a force of 4.9x105 N. How much time is needed to accelerate the projectile? Problem 4.14: A 41 kg box is thrown at 220 m/s against a barrier. It is brought to a halt in 6.5 ms. What is the average net force that acts on the box? m = 1300 kg Wind Paddling Paddling: force FP of 17 N, to east Wind: force FW of 15 N, 67o north of east Find ax, ay for the raft. The net force is: Problem 4.17: A 325 kg boat is sailing 15.0 degrees north of east at 2.00 m/s. 30 s later, it is sailing 35.0 degrees north of east at 4.00 m/s. During this time, three forces act on the boat: Auxiliary engine : F1 31.0 N to 15.0 degrees north of east Water resistance: F2 23.0 N to 15.0 degrees south of west Wind resistance : Fw Find the magnitude and direction of the force Fw . Give the direction with respect to due east. Apply Newton’s Second Law: F1 F2 Fw ma First, find the average acceleration : north vi 2 m/s 15 vf 4 m/s 35 east t 30 sec vf vi v vf vi Then use Newton’s second law: north m a 24.1 N 15 F2 23 N Fw ? F1 31 N ? east F1 F2 8N