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The Laws of Motion

The Laws of Motion. …or, Newtonian mechanics. The Laws of Motion. …or, Newtonian mechanics. Where is this sculpture from?. Isaac Newton. Newton believed that mathematics can describe nature, accurately.

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The Laws of Motion

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  1. The Laws of Motion …or, Newtonian mechanics ISP 209 - 2A

  2. The Laws of Motion …or, Newtonian mechanics ISP 209 - 2A

  3. Where is this sculpture from? Isaac Newton Newton believed that mathematics can describe nature, accurately. He solved the premier scientific problem of his day – to explain the motion of the planets. ISP 209 - 2A

  4. Newton’s Laws of Motion • The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0. • Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma. • Action and reaction. For every action there is an equal but opposite reaction. ISP 209 - 2A

  5. Atwood machine with equal weights Net force = 0 implies constant velocity. ISP 209 - 2A

  6. Newton’s second law of motion F = m a • F = force acting on the moving object, a vector • m = mass of the moving object • a = acceleration of the moving object, a vector If the force is known, Newton’s second law states how the object (on which the force is acting) accelerates: ISP 209 - 2A

  7. Understanding vectors A vector is a mathematical quantity that has both a magnitude and a direction. F = m a an equation of vectors ISP 209 - 2A

  8. Three kinds of acceleration m speeds up m slows down m changes direction Example: Circular motion has centripetal acceleration and centripetal force; F = ma. ISP 209 - 2A

  9. Quantitative applications of F = ma ISP 209 - 2A

  10. Mass is a property of matter = quantitative measure of inertia. The standard unit of mass is the kilogram (kg). A gram is 0.001 kg. This picture shows the international prototype 1 kg mass standard. It is a platinum-iridium cylinder kept in Sevres, France. Any physical object has a mass m, which could be measured against a standard, e.g., using a balance. ISP 209 - 2A

  11. Force = a push or a pull exerted on one object by another object. The standard unit of force is the newton (N). The newton is defined in terms of more fundamental units by 1 N = 1 kg m/s2 (consistent with F = m a) ISP 209 - 2A

  12. Acceleration and Force Given the mass of the object, and given the force that is acting on it, the acceleration is If necessary, identify a and F as vectors and take into account their direction (both in the same direction!) ISP 209 - 2A

  13. Example. Playing catch with a softball The trajectory has 3 parts. free fall the throw the catch What is the force acting on the ball, during each part of the trajectory? ISP 209 - 2A

  14. Example Problem A dragster accelerates from 0 to 60 mi/hr in 6 seconds. Calculate the force on the car if the mass is 103 kg. Answer: 4.47 x 103 N ISP 209 - 2A

  15. Two examples of forces • weight (the force of gravity on an object) • string tension (the force exerted by a taut string) ISP 209 - 2A

  16. F If released, the acceleration of m would be … By Newton’s second law the force on m must be … Gravity What is the force acting on the mass m due to the Earth’s gravity? Solution g = 9.81 m/s2 That is, the magnitude, or strength, is mg and the direction is downward. By the way, what is the reaction force? ISP 209 - 2A

  17. force of gravity newtons kg Weight = the force of gravity The weight of an object is, by definition, the strength of the force of gravity pulling the objectdownward. W = m g ISP 209 - 2A

  18. Example: What is the weight of a 1 kg mass near the Earth’s surface? W = mg = 9.81 N Or, W = 2.21 pounds ISP 209 - 2A

  19. Mass and Weight  different! ► Mass is an intrinsic property of an object. It is completely determined by the number and type of atoms that make up the object. It does not depend on the environment in which the object is located. ► But weight is different. Weight depends on both the object itself, and on some other object that exerts the gravitational force. So, for example, the mass of an object would be the same on the moon or the Earth; but the weight would be different. ISP 209 - 2A

  20. An astronaut would not need a car jack to change a flat tire on the Moon Buggy. ISP 209 - 2A

  21. Analyze free fall including air friction The aerodynamic drag force (C) depends on the size, shape and surface roughness; it is about the same for both balls. • The gravitational acceleration (g) is independent of mass. • Effect of air is inversely proportional to mass: • heavy --- small effect of air • light --- large effect of air ISP 209 - 2A

  22. String tension • The force exerted by the string, at either end: • direction is parallel to the string • magnitude (same at both ends) is called the tension Example. Suppose a string can withstand string tension 500 N without breaking. What is the maximum mass M that it can hold suspended in Earth’s gravity? Answer: 51.0 kg ISP 209 - 2A

  23. Analyze the motion of a pendulum. Solve by calculus. ISP 209 - 2A

  24. More example problems 3. A gymnast weighs 100 pounds. (a) What is her weight in newtons? (b) What is her mass? 445 N 45.3 kg 4. A car of 2000 pounds moving 30 mi/hr crashes into a brick wall. The collision lasts 0.3 seconds. Calculate the force acting on the car during the collision. Express the answer in both newtons and pounds. 4.05 x 104 N or 9,100 pounds ISP 209 - 2A

  25. differential equation Newton’s second law and calculus Isaac Newton invented calculus to solve the equations of motion; i.e., to calculate motion for the force that is acting. Generally, calculus is the mathematics that describes continuous change. ISP 209 - 2A

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  27. Quiz Question A car accelerates away from a stop sign with acceleration 0.1 g ( = 0.981 m/s2). The mass of the driver is 50 kg. What is the force on the driver? (Be sure to include the unit of measurement!) ISP 209 - 2A

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