Newtonian DYNMICS (Newton’s Laws)

1. Newtonian DYNMICS (Newton’s Laws) Corresponding Activities: Discuss Forces Complete Worksheet Isaac Newton’s work represents one of the greatest contributions to science ever made by an individual. Most notably, Newton derived the law of universal gravitation, invented the branch of mathematics called calculus, and performed experiments investigating the nature of light and color.

2. Lecture outline: Comparison between kinematics and dynamics as the branches of physics (mechanics) The Language of Dynamics Description of interaction between the objects Newton’s 1st law: the Law of Inertia Newton’s 2nd law: cause and effect law Application of Newton’s laws to problem solving Lecture outcomes: You will learn how to: Identify and denote forcesacting on an object Draw aFree Body Diagram(FBD) Use a FBD to write an equation of motion You will understand the meaning of Newton’s 1st and 2nd laws: via making everyday life connections Via doing testing experiments (making predictions) You will practice problem solving applied to: Applications of Newton’s 1st and 2ndlaws of motion. Lecture Outline and Outcomes Created by Dr. Marina Milner-Bolotin Lecture #7

3. I. Observations: Newtonian Dynamics • Goal:Descriptionof motion • Questions answered by Kinematics: • How far? How fast? How long does it take? When (i.e. meeting time and place)? Where is an object going to be at a certain time? • Questions answered by Dynamics: • Why is the object moving in a certain way? What causes the object to change its velocity? How the interaction between objects influence their motion? • Dynamics studies motion at a deeper level than kinematics: it studies the causes of changes in objects’ motion! Created by Dr. Marina Milner-Bolotin Lecture #7

4. The Language of Dynamics • Force: The measure of interaction between two objects (pull or push). It is a vector quantity – it has a magnitude and direction, the unit of force is Newton, N • Mass: The measure of how difficult it is to change object’s velocity (sluggishness or inertia of the object). It is a scalar. SI unit of mass is a kilogram, kg • Weight: The force the Earth is pulling the object with. Weight is a vector quantity, it has a magnitude and direction, the unit of weight is Newton, N Created by Dr. Marina Milner-Bolotin Lecture #7

5. A Force as an Interaction Between Two Objects The Meaning of a Net Force: One object can interact with many. So many forces can be exerted on it. Right now, at least 2 forces are acting on you: the Earth is pulling you downwards and a chair pushing you upwards. A NET FORCE(Fnet) is a resultant force acting on an object. To find the resultant force (Fnet) you have to add up all the forces acting on an object. (Remember, forces are vector, so take into account their directions & magnitudes) A spring scale shows the strength of the interaction between the Earth and the object. The stronger the interaction is, the more it stretches! The force of attraction between the Earth and the object is called WEIGHT of the object. We can measure weight in lbs or in Newtons: 1 lbs = 4.45 N Created by Dr. Marina Milner-Bolotin Lecture #7

6. 3 N 4 N m N W E S PRS 7-1: Figuring out the Net Force Find magnitude and direction of the net force acting on an object of mass m. Explain your answer. • 1 N North-East • 3 N North • 4 N East • 5 N East • 5 N North-East • 7 N North-East Created by Dr. Marina Milner-Bolotin Lecture #7

7. Newton’s 1st Law: The Law of Inertia • An object at rest remains at rest as long as no Fnetacts on it • An object moving with constant velocity continues to move with the same speed and in the same direction (the same velocity) as long as no net force acts on it • Every object continues in its state of rest, or uniform motion in a straight line, unless it is compelled to change that state by unbalanced forces impressed upon it • Inertia is a property of objects to resist changes is motion! An additional force is NOT required to keep a cart moving with a constant speed on a frictionless track! Created by Dr. Marina Milner-Bolotin Lecture #7

8. Why Is the 1st Law So Important? • The 1st law holds true only in the non-accelerating reference frames which will be called INERTIAL REFERENCE FRAMES (IRF) • Newton’s laws work only in IRF, for other frames of reference modifications must be made! • For instance, an accelerating car or train or elevator are not an IRF (think why you need seat belts in your car!) • Our Earth is not an exactly IRF due to its rotation and annual motion. However, we will treat the Earth as an IRF! For the experimental accuracy we need, this approximation is good enough! Created by Dr. Marina Milner-Bolotin Lecture #7

9. PRS 7-2: Newton’s 1st Law In which of the following cases a net force acting on an object (Fnet) is zero? Explain. • You are speeding up from 50 km/h to 65 km/h • You are slowing down from 65 km/h to 55 km/h • You are turning left at constant speed of 25 km/h • You are making a U-turn at constant speed of 15 km/h • You are turning right while slowing down from 50 km/h to 30 km/h • None of the above Created by Dr. Marina Milner-Bolotin Lecture #7

10. Newton’s 2nd Law: Cause & Effect Law • Only unbalanced forces cause object to accelerate. • An object of mass m has an acceleration a, equal to the net force SF, divided by the mass of the object, m. Created by Dr. Marina Milner-Bolotin Lecture #7

11. F table on book F Earth on book Drawing Free Body Diagram - FBD • Denoting forces: • A force has to have: • a magnitude and direction (an arrow); • two indices: • F Earth on Dr. M • F Dr. M on the floor • F chair on your … Created by Dr. Marina Milner-Bolotin Lecture #7

12. Physics Problem Solving Tips Problem solving tips: Sketch the forces (indices!) Choose a system (object) of interest Choose and draw a coordinate system Resolve the forces into components Write the equations Created by Dr. Marina Milner-Bolotin Lecture #7

13. Bridging Kinematics and Dynamics Kinematics Question - Quantity Where? - Position When? - Clock reading For how long? - Time interval How fast? - Velocity, speed, Acceleration Dynamics Question - Quantity How much matter? - Mass How strong is the interaction? - Force What is the effect of the interaction? - Acceleration Created by Dr. Marina Milner-Bolotin Lecture #7

14. v0= 60 mi/h vf = 0 mi/h x 50 m Example 1: Braking Force (1-D case) A twenty-ton-train cart is moving at 60 mi/h (27 m/s). What braking force is needed to stop the cart in 50 meters? Given: v = 60 mi/h = 27 m/s Dx = 50 m Force - ? Notice, during the exam you will need to know how to convert km/h or mi/h into m/s. Please practice your conversions! Created by Dr. Marina Milner-Bolotin Lecture #7

15. Detailed Solution We know the mass of the cart but how can we find its acceleration? To find acceleration we have to use our knowledge of kinematics. If we know the stopping distance and the initial velocity, we can find acceleration! Created by Dr. Marina Milner-Bolotin Lecture #7

16. References and HW Resources: • Chapter 4, textbook: Physics by D. Giancoli • Related activities: Tutorial 3, HW Problems posted on the website: Set 3. • Use ActivPhysicssoftware (www.aw.com/young11) and sign up for Mastering Physics (www.masteringphysics.com) if you want to practice more and get instantaneous feedback. • Voltaire’s (1694-1778) letters on Newton: http://www.fordham.edu/halsall/mod/1778voltaire-newton.html • Isaac Newton: http://www.newton.cam.ac.uk/newtlife.html Created by Dr. Marina Milner-Bolotin Lecture #7