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PHYSICS FOR ENGINEERS We’ll use the book from P.A. Tipler ... and some more resources from the web 1 Dynamics 07 - 2nd week NEWTON’S LAWS First law. An object at rest stays at rest unless acted on by an external force. An object in motion continues to travel with constant velocity unless acted on by an external force. act on influir sobre Remark: Also called the "law of inertia," Newton's first law states that a body at rest remains at rest and a body in motion continues to move at a constant velocity unless acted upon by act upon influir sobre, afectar an external force. Second law. A net force F acting on a body gives it an acceleration a which is in the direction of the force and has magnitude inversely proportional to the mass m of the body. F ma Momentum: for a single particle of mass m with velocity v, the momentum is defined as p mv From Newton's second law, a force F produces a change in momentum Which are the SI units of force and momentum? dp F dt stand for simbolizar, ser las siglas de agree upon estar de acuerdo, concertar 2 "SI" stands for "System International" and is the set of physical units agreed upon by international convention Dynamics 07 - 2nd week Example. How much horizontal net force is required to accelerate a 1200 kg car at 2 m·s-2 from the rest on a horizontal plane? 1200 kg 2 m·s-2 F ma 2400 N To do yourself: Example 4-1 (5 min) To do yourself: Example 4-2 (5 min) strand varar, dejar desamparado To do yourself: Example 4-3 (5 min) For you to read: The Force Due to Gravity: Weight (15 min) Exemple. A box on a lift The box is inside a lift Let W0 be the weight of the box The lift accelerates upwards, let a be its acceleration a Which is then the apparent weight of the box? W0 mg W0 Which is the apparent weight of the box in case the lift moves up with a constant velocity? 3 Dynamics 07 - 2nd week Also related with Newton’s second law: impulse. An impulse is an instantaneous change in momentum dp mdv which can be found by integrating a force F over a characteristic time t, giving dp F dt t p Fdt Which S.I. units do we use for impulse? Can you pose some exemples on impulse? 0 Also related with Newton’s second law: friction forces. http://www.sc.ehu.es/sbweb/fisica/dinamica/rozamiento/general/rozamiento.htm Third law. Whenever a body exerts a force on another body, the latter exerts a force of equal magnitude and opposite direction on the former. This is known as the law of action and reaction. A well knowing horse To do yourself: Exemple 4-11 (5 min) 4 Dynamics 07 - 2nd week FRICTION FORCES Static Kinetic 5 Dynamics 07 - 2nd week FREE-BODY DIAGRAMS A diagram that shows schematically all forces acting on a system, is called free-body diagram. It is called free-body diagram because the body is drawn free from (without) its surroundings. To do yourself: Example 4-6 (10 min) 6 Dynamics MORE PROBLEMS 07 - 2nd week Find out the acceleration: Atwood’s Machine (consider an ideal pulley) What about the tension of the rope? T To do yourself: Example 4-9 (10 min) To do yourself: Example 4-10 (10 min) The block m2 has an inhabitant:it has a hollow, which is the home of a bug. T T 2m1m2 g m1 m2 m1 To do yourself: Example 4-12 (10 min) m2 m1g m2g +) F1 T m1 g m1a F2 m2 g T m2a m2 m1 g m1 m2 a a m2 m1 g m1 m2 Let mb be the mass of the bug. What about its weight when it is at home? Try it yourself! 7 Dynamics 07 - 2nd week SOME MORE QUESTIONS & PROBLEMS kick Question: dar patadas hurt hacer daño An astronaut on Earth kicks a bowling ball and hurts his foot. A year later, the same astronaut kicks the same bowling ball on the moon with the same force. His foot hurts... (a) (b) (c) more less the same The masses of both the bowling ball and the astronaut remain the same, so his foot will feel the same resistance and hurt the same as before. Question: Where (the Earth or the Moon) is easier for the astronaut to pick up the bowling ball from the floor? The weights of the bowling ball and the astronaut are less on the Moon... Thus it would be easier for the astronaut to pick up the bowling ball on the Moon than on the Earth. 8