1. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Physics I 95.141 LECTURE 6 9/22/10

2. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Exam Prep Problem A rock is launched with an initial speed v o =22m/s at an angle θ o =65º from the origin. Ignore air resistance. –A)(10pts) Draw a coordinate system for this problem and show the trajectory of the rock. Give the initial velocity vector of the rock in component form. –B) (8pts) How high does the rock go and how long does it take the rock to get to that height? –C) (7pts) How far, horizontally, will the rock travel before it lands?

3. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Exam Prep Problem A rock is launched with an initial speed v o =22m/s at an angle θ o =65º from the origin. Ignore air resistance. –A)(10pts) Draw a coordinate system for this problem and show the trajectory of the rock. Give the initial velocity vector of the rock in component form.

4. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Exam Prep Problem A rock is launched with an initial speed v o =22m/s at an angle θ o =65º from the origin. Ignore air resistance. –B) (8pts) How high does the rock go and how long does it take the rock to get to that height?

5. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Exam Prep Problem A rock is launched with an initial speed v o =22m/s at an angle θ o =65º from the origin. Ignore air resistance. –B) (7pts) How far, horizontally, will the rock travel before it lands?

6. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Administrative Notes HW review Session Tonight –6:30 pm, OH 218 Structure of HW Review Sessions –Why we do it this way –Why it is important to try Structure of this course –Combination of your effort/our effort Lecture Notes Practice exams/prep problems Attendance Policy

7. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Outline Force Newton’s 1 st Law Newton’s 2 nd Law Newton’s 3 rd Law What do we know? –Units –Kinematic equations –Freely falling objects –Vectors –Kinematics + Vectors = Vector Kinematics –Relative motion –Projectile motion

8. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Force Intuitively, we understand a Force to be a push or pull on an object –This could be a racket hitting a ball, elevator cable pulling on a car, a locomotive pulling a train… These are all contact forces, where the force is exerted by one object in contact with another –Force can also be exerted by magnets, electric fields, or gravity Here, Force is exerted by a field, not an object, but this is still a force! Force has magnitude and direction: it is a VECTOR!

9. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Force In order for something at rest to start moving, a Force must be exerted on it. However, if something is already moving, you also need a Force acting on it to stop motion!

10. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Inertia Obviously, some things are harder to get moving than others… If you had to choose whether to carry an ice skater or an offensive lineman up to the Dean’s office on the 5 th floor: which do you think would be easier? We quantify inertia with a measure we call mass SI units: mass  [kg]

11. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Newton’s 2 nd Law If Newton’s first law tells us how an object behave with no Force, we also want to understand how an object behaves with a Force applied. The acceleration of an object is directly proportional to the net force applied to the object, and the constant of proportionality is mass.

12. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Units for Force Using Newton’s 2 nd Law, we can figure out the units of Force.

13. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Redefine Force An action capable of accelerating an object Acceleration is a vector, as is Force. Net acceleration is in the same direction as net Force.

14. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Example Problem A 1500kg car traveling at 100km/h needs to stop in 55m. What force is required? Draw diagram Determine coordinate system

15. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Example Problem A 1500kg car traveling at 100km/h needs to stop in 55m. What force is required? Knowns/Unknowns (UNITS)

16. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Example Problem A 1500kg car traveling at 100km/h needs to stop in 55m. What force is required? Choose equations and solve

17. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Connection between Newton’s 1 st, 2 nd Laws If F=ma And no Force is exerted on an object How can we describe the object’s velocity?

18. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Newton’s 2 nd Law Do Newton’s 1 st and 2 nd Law work every where? –Say you are in a pickup truck that is accelerating, and you put a frictionless block in the back. –What do you see happening to the block?

19. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Newton’s 2 nd Law Do Newton’s 1 st and 2 nd Law work every where? –Say you are in a pickup truck that is accelerating, and you put a frictionless block in the back. –What is the Force causing this?

20. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Newton’s 2 nd Law Do Newton’s 1 st and 2 nd Law work every where? –Say you are in a pickup truck that is accelerating, and you put a frictionless block in the back. –What does someone on the ground see?

21. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Inertial Reference Frames Newton’s Laws only work in Inertial reference frames Inertial reference frame –One in which Newton’s Laws hold –A Reference Frame that moves with a constant velocity –A Reference Frame at rest

22. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Newton’s 3 rd Law of Motion 1 st Law: Law of Inertia, things want to keep on doing what they are already doing. 2 nd Law: Forces cause objects to accelerate, with a=F/m. But where do forces come from? –Forces come from other objects Hammer exerts a force on the nail The Earth exerts a force on a falling ball (gravity) Elevator cable exerts force on car…

23. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Newton’s 3 rd Law But when hammer hits nail, it stops very quickly. This is deceleration, which means the nail must also exert a Force on the hammer. This is Newton’s 3 rd Law –Whenever one object exerts a Force on a second object, the second object exerts an equal Force in the opposite direction. –Sometimes, you hear: “For every action, there is an equal and opposite reaction” –Remember though, the action and reaction act on different objects!

24. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Action/Reaction They actually get the Physics right here! For every Force exerted on an object, there is an equal and opposite force exerted by that object

25. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Describing Forces When we talk about Forces, it is very important that we describe the Force as “exerted by” something and “acting on” another thing. –For instance, in the case of the ice skater, force is exerted on the skater by the ice. –For the car, the Force making the car move is exerted by the ground on the tires. When we start solving problems, it is important to keep this straight. If you are interested in the motion of an object, you only want to sum up the Forces acting on that object. For a person walking, the ground is what moves the person forward.

26. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 The Motivator

27. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Draw Diagram Want F, need to figure out acceleration –Assume T f =0.25s M=60kg Δx=1.8m Δy=-1m 1.8m 1m

28. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Projectile Motion Problem (I) What is initial launch velocity?

29. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 Acceleration If we know the initial launch velocity, then we know the final velocity after acceleration –Initial velocity of part II = final velocity of part I

30. Department of Physics and Applied Physics 95.141, F2010, Lecture 6 What Did We Learn Newton’s Laws –Law of Inertia –F=ma –Action/Reaction Solving basic Force problems How to describe motion of an object with Force applied.