Announcements: Midterm 1 in less than a week, Sept. 19 (Chapter 1-6)

1. Announcements: • Midterm 1 in less than a week, Sept. 19 (Chapter 1-6) • Can use a 3x5 inch cheat card with 10 formulas • I will post practice test on the Web • HW 10 is due on Friday, Sept. 23, 10 pm • Extended office hours this Friday 1-3

2. Chapter 6: Force and Motion - II Reading assignment: Chapter 7.1-7.5 Homework : Due Friday Sept 23, 2005 (an extra week to do it! Chapter 7: Q13, 4, 9, 18, 22, 29 • In this chapter we will learn about • static friction • kinetic friction • centripetal force • kinetic drag force

3. Black board example 5.6 • Two objects of mass m1 and m2 are attached by a string over a pulley as shown in the Figure. m2 lies on an incline with angle q. • Determine the magnitude of the acceleration of the two objects and the tension in the cord. • m1 = 10.0 kg, m2 = 5.00 kg, q = 45º

4. Forces of Friction • Static friction, fs • Kinetic friction, fk

5. The following laws hold true about friction: • Friction force, f, is ________________ to normal force, n. • ms and mk: coefficients of ___________ and ____________ friction, respectively • Direction of frictional force is ______________ to direction of relative motion • Values of ms and mk depend on nature of surface. • ms and mk don’t depend on the ________ of contact • ms and mk don’t depend on ____________. • Friction is due to the surfaces interacting with each other on the microscopic level (sliding over bumps, chemical bonds)

6. Black board example 6.1 Measuring the coefficient of static friction A brick is placed on an inclined board as shown in the figure. The angle of incline is increased until the block starts to move. • Determine the static friction coefficient from the critical angle, qc, at which the block starts to move. • What is ms if the block starts sliding at qC = 31°

7. Black board example 6.2 Measuring the coefficient of kinetic friction A hockey puck is given an initial speed of 20.0 m/s. It slides 115 m before coming to rest. • Determine the coefficient of kinetic friction between the puck and the ice. • Could the coefficient of friction be larger than 1?

8. Thus far we have applied Newton’s law, F = m*a to linear motion. Now we’ll apply it to rotational motion

9. Particle moving with __________ speed v in a circular path with radius r has an acceleration ar: (Derivation: see Chapter 4.7) • The acceleration points towards the _________ of the circle! • Centripetal acceleration

10. Newton’s law along the radial direction (along r):

11. Uniform Circular motion: • The velocity of the particle is along the __________ • The centripetal acceleration is towards the __________ • The centripetal force acting on the particle is towards the ________ • Centripetal force causes a change in the ________________ but no change in ________________. The magnitude of the centripetal acceleration is: a =______________ Newton’s law: The force on the particle is (centripetal force) F= m·a = ______________

12. A particle is moving in a circular path. If the force on the particle would suddenly vanish (string cut) in which direction would the ball fly off?

13. Black board example 6.3 Franz rotates a stone (m = 0.50 kg) that is attached to the end of a 1.5 m cord above his head in a horizontal circle. If the cord can hold 50 N of tension, at what maximum speed will it rupture. Which force “provides” the centripetal force?

14. Black board example 6.4 Jeff Gordon leads his race and must drive into a curve at top speed to win it all. The radius of the curve is 1000.0 m and the coefficient of static friction between his tires and the dry pavement is 0.500. Find the maximum speed he can have and still make the turn. Which force “provides” the centipetal force?

15. Motion in the presence of drag (or ________) forces Motion in ________ media.

16. Objects interact with the medium through which they are moving. • Air • Water, oil, liquids. The drag forces depend on the ________ of the object. F ~ v: Objects falling in __________, tiny objects falling in air. F ~ v2: ________________ objects moving in air.

17. Terminal velocity. When the ___________ force of the falling object is equal to the _________________ force on the object. • Examples: • - skydivers • soap bubbles falling in air • small spheres dropping in liquid.

18. Air drag at high speeds. For objects moving at high speeds through air: Drag force: Where: ___… Drag coefficient of object (depends on shape) ___…density of air A… cross-sectional area of object v… velocity of object

19. Black board example 6.5 • A careless person drives a pick-up truck with a mattress tied to the roof. The mattress is 50 cm high and 150 cm wide. • Calculate the resistive force acting on the mattress if the truck drives with a speed of 30 m/s (67 mi/hr). • Should the driver worry about his load if it is tied down with a rope capable of holding 250 N? Drag coefficient = 0.5 density of air = 1.29 kg/m3

20. Air drag at high speeds. For objects moving at high speeds through air: Drag force: Where: C… Drag coefficient of object (depends on shape) r…density of air A… cross-sectional area of object v… velocity of object

21. Black board example 6.5 • A careless person drives a pick-up truck with a mattress tied to the roof. The mattress is 50 cm high and 150 cm wide. • Calculate the resistive force acting on the mattress if the truck drives with a speed of 30 m/s (67 mi/hr). • Should the driver worry about his load if it is tied down with a rope capable of holding 250 N? Drag coefficient = 0.5 density of air = 1.29 kg/m3