Physics I 95.141 LECTURE 7 9/27/10

1. Physics I95.141LECTURE 79/27/10

2. Exam Prep Problem • A 2kg mass sits on a frictionless table, travelling with an initial velocity at t=0. A constant Force of is applied to this mass at t=0. • A) (5pts) What is the acceleration of the mass for t>0s? • B) (5pts) At what time does the y component of velocity go to 0? • C) (5pts) At what time does the x component of velocity go to 0? • D) (10pts) What is the displacement of the mass after 5s?

3. Exam Prep Problem • A 2kg mass sits on a frictionless table, travelling with an initial velocity at t=0. A constant Force of is applied to this mass at t=0. • A) (5pts) What is the acceleration of the mass for t>0s?

4. Exam Prep Problem • A 2kg mass sits on a frictionless table, travelling with an initial velocity at t=0. A constant Force of is applied to this mass at t=0. • B) (5pts) At what time does the y component of velocity go to 0?

5. Exam Prep Problem • A 2kg mass sits on a frictionless table, travelling with an initial velocity at t=0. A constant Force of is applied to this mass at t=0. • C) (5pts) At what time does the x component of velocity go to 0?

6. Exam Prep Problem • A 2kg mass sits on a frictionless table, travelling with an initial velocity at t=0. A constant Force of is applied to this mass at t=0. • D) (10pts) What is the displacement of the mass after 5s?

7. Force Review Problem • Superman must stop a 4x105kg train traveling at 80m/s in 320m. • What Force must he exert to do this?

8. Outline • Force of Gravity and Normal Force • Free Body Diagrams • Problem Solving • What do we know? • Units • Kinematic equations • Freely falling objects • Vectors • Kinematics + Vectors = Vector Kinematics • Relative motion • Projectile motion • Newton’s Laws

9. Force of Gravity • If something is accelerating, that means there must be a force on it. In this case, that Force is the gravitational force. • Magnitude of this force is known as weight. • We know that, ignoring air resistance, all objects dropped near the surface of the Earth will accelerate with

10. Example Problem I(a) • A upwards Force is exerted on a mass of 2kg. What is the acceleration of the mass if the Force is • A) 10N? 2kg

11. Example Problem I(b) • A upwards Force is exerted on a mass of 2kg. What is the acceleration of the mass if the Force is • B) 19.6N? 2kg

12. Example Problem I(c) • A upwards Force is exerted on a mass of 2kg. What is the acceleration of the mass if the Force is • C) 40N? 2kg

13. Force of Gravity • This force is always acting on objects at the surface of the Earth. • Why don’t we see everything accelerating downwards towards the center of the Earth? • There is another force acting on the object. And since the acceleration of the resting object is 0, this force must be equal to the Force of gravity.

14. The Normal Force • The Normal Force acts perpendicular to the surface exerting it. Normal=perpendicular. • The Normal Force is NOT always vertical. It is perpendicular to the surface. If the surface is not horizontal, the Normal Force isn’t vertical.

15. Example II(a) • For a mass M at rest on a flat surface, we can determine the Normal Force for 3 different situations: • A) Box on flat surface

16. Example II(b) • For a mass M at rest on a flat surface, we can determine the Normal Force for 3 different situations: • B) Box on flat surface, hand pushing down -FH

17. Example II(c) • For a mass M at rest on a flat surface, we can determine the Normal Force for 3 different situations: • C) Box on flat surface, hand pulling up +FH<mg

18. Solving Force Problems • FREE BODY DIAGRAMS • If we are interested in the motion of an object, then we need to know the NET FORCE acting on that object!!

19. Example Problem III • My kids are fighting over a 0.5kg toy resting on a table (xy plane). • My son pulls with a force: and my daughter with a force of: Find the net Force on the object, and its acceleration. • Draw Free Body Diagram • Find Net Force • Find Acceleration

20. Comments on Example Problem III • What happened to the Normal Force and the Force of gravity in this problem? • What about friction, air resistance, etc.?

21. Example IV • Two boxes are held together by a cable and pulled by a string on a frictionless table. • A) Find acceleration of each box • B) Tension in cord

22. Example IV • Choose coordinate system • Free Body Diagrams for each box

23. Example IV • How do we handle the connecting (massless) cord?

24. Example IV • Sum Forces

25. Example IV • Solve system of equations

26. Free Body Diagrams • For any object subject to a Force, we can always draw a free body diagram. • When we choose coordinate system, we want to choose carefully…

27. Boxes on Inclines • Now suppose we have a box of mass M on a frictionless inclined plane… • Coordinate system θ

28. Boxes on Inclines • Now suppose we have a box of mass M on a frictionless inclined plane… • Free Body Diagram θ

29. Boxes on Inclines • Divide Forces into x, y components θ Φ

30. Boxes on Inclines • What is Φ?

31. Boxes on Inclines • Divide Forces into x, y components θ θ

32. Example V • A 10 kg box sits on a frictionless inclined plane (θ=30º). • What is the Normal Force on the box? • What is the box’s acceleration? • Draw diagram and choose coordinate system

33. Example V • A 10 kg box sits on a frictionless inclined plane (θ=30º) • Free body diagram • Divide Forces into x, y

34. Example V • A 10 kg box sits on a frictionless inclined plane (θ=30º) • Solve for acceleration

35. Problem Solving approach • Draw Diagram • Choose coordinate system • Draw Free Body Diagram • Determine Force components • Write equations of motion • Solve