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Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 13, 14, 15 Newton’s Laws 1st Law: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration 2nd Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. 3rd Law: For every action there is an equal, but opposite reaction Newton’s law of gravitation Falling with air resistance dv 2 a g kv dt Terminal Velocity with Coffee Filters mg Fr ma where Fr is the resistance force. Fr ag m 1. A penny and a quarter dropped from a ladder land at the same time (air resistance is negligible). 2. A coin dropped in a coffee filter from a ladder lands later coffee filter (the terminal velocity is than a coin without smaller for larger cross-section area). 3. A quarter dropped in a coffee filter will land faster than a penny in a coffee filter (the terminal velocity is larger for larger mass) 4. Two identical coins dropped in coffee filters of different diameters land at different times (the terminal velocity is smaller for larger cross-section area). Resistance force: Fr Av 2 A – area of the projectile 2 4 0.25 N s /m For a spherical projectile in air at STP: Terminal velocity: Fr ag 0 m Fr mg Av 2 mg vT mg A A 70-kg man with a parachute: vT ~ 5 m/s A 70-kg man without a parachute: vT ~ 70 m/s Newton’s st 1 Law A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration Aristotle: a natural state of an object is at rest; a force is necessary to keep an object in motion. It follows from common sense. 384-322 B.C. Galileo: was able to identify a hidden force of friction behind commonsense experiments 1564-1642 Galileo: If no force is applied to a moving object, it will continue to move with constant speed in a straight line Inertial reference frames Galilean principle of relativity: Laws of physics (and everything in the Universe) look the same for all observers who move with a constant velocity with respect to each other. Kinetic Friction • For kinetic friction, it turns out that the larger the Normal Force the larger the friction. We can write FFriction = mKineticN Here m is a constant • Warning: – THIS IS NOT A VECTOR EQUATION! Static Friction • This is more complicated • For static friction, the friction force can vary FFriction mStaticN Example of the refrigerator: – If I don’t push, what is the static friction force? – What if I push a little? Coefficient of friction: m H What is the normal force? What is the velocity of the block when it reaches the bottom? Newton’s rd 3 Law For every action there is an equal, but opposite, reaction Skater • Skater pushes on a wall • The wall pushes back – Equal and opposite force • The push from the wall is a force – Force provides an acceleration – She flies off with some non-zero speed P P No friction m1 m1 m2 Free body diagram N1 F12 F21 m1 N2 m2 m2g m1g F12=F21 Quiz a) A crate of mass m is on the flat bed of a pick up truck. The coefficient of friction between the crate and the truck is m. The truck is traveling at the constant velocity of magnitude V1. Draw the free body diagram for the crate. b) The truck starts to accelerate with an acceleration ac. Draw the free body diagram for the crate, if the crate does not slip. A small block, mass 2kg, rests on top of a larger block, mass 20 kg. The coefficient of friction between the blocks is 0.25. If the larger block is on a frictionless table, what is the largest horizontal force that can be applied to it without the small block slipping? F N1 N2 mN1 mN1 F N1 m1 g m2 g A block of mass 20 kg is pushed against a vertical surface as shown. The coefficient of friction between the surface and the block is 0.2. If θ=300, what is the minimum magnitude of P to hold the block still? P θ V0 A block of mass m is given an initial velocity V0 up an inclined plane with angle of incline θ. Find acceleration of the block if a) m = 0 b) non-zero m A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge and a horizontal force F is applied to the wedge. What must the magnitude of F be if the block is to remain at a constant height above the tabletop? F A Problem With First Year Physics Strings and Pulleys m1 m1, m2 are given m2>m1 String is massless and unstretchable m2 Find accelerations of m1 and m2 (assume no friction in pulley) Block 1, of mass m1, is placed at rest on an inclined plane. It is attached by a massless, unstretchable string to block 2, of mass m2. The pulley is massless and frictionless and just changes the direction of the tension in the string. The coefficient of friction between the plane and m1 is the constant m. 1 2 Determine what range of values for mass m2 will keep the system at rest. Find acceleration if mass 2 goes down. Friction everywhere. 2 F 1 Find F necessary to drag the box 1 at constant speed. The advantage of a pulley What minimum force F is needed to lift the piano of mass M? The Elevator Problem Have a great day! Reading: Chapter 7 Hw: Chapter 6 problems and exercises