Chapter 6 Force and Motion II

1. Chapter 6 Force and Motion II 6.2. Friction       6.3. Properties of Friction       6.4. The Drag Force and Terminal Speed       6.5. Uniform Circular Motion      

2. The Friction Force There are two types of friction forces: • Kinetic Friction Forces • Static Friction Forces

3. Kinetic Friction Forces An object is experiencing a kinetic friction force when the object is moving relative to a surface. • Kinetic friction forces is linearly proportional to the normal force. • The slope of Kinetic friction forces vs. the normal force is changing for different surfaces.

4. Kinetic Friction Forces The magnitude of the kinetic friction force can be expressed as: The slope μkin is called the coefficient of kinetic friction and N is the magnitude of the normal force.

5. Question A person has a choice of either pushing or pulling a sled at a constant velocity, as the drawing illustrates. Friction is present. If the angle θis the same in both cases, does it require less force to push or to pull? Account for your answer.

6. Example 1Sled Riding A sled is traveling at 4.00 m/s along a horizontal stretch of snow, as Figure illustrates. The coefficient of kinetic friction is μk=0.0500. How far does the sled go before stopping?

7. Static Friction Forces An object is experiencing a static friction force when the object intend to move (but not move yet) relative to the surface.

8. Properties of Static Friction Forces • The magnitude fs of the static frictional force can have any value from zero up to a maximum value of depending on the applied force. • The maximum static friction is: The μs is the coefficient of static friction, and N is the magnitude of the normal force. • The coefficient of static friction is usually larger than the coefficient of kinetic friction

9. Example 2The Force Needed to Start a Sled Moving A sled is resting on a horizontal patch of snow, and the coefficient of static friction is μs=0.350. The sled and its rider have a total mass of 38.0 kg. What is the magnitude of the maximum horizontal force that can be applied to the sled before it just begins to move?

10. Example 3 A House on a Hill A house is built on the top of a hill with a nearby 45° slope (Fig. 6-42). An engineering study indicates that the slope angle should be reduced because the top layers of soil along the slope might slip past the lower layers. If the static coefficient of friction between two such layers is 0.5, what is the least angle φthrough which the present slope should be reduced to prevent slippage?

11. Example 4 Block on a Slab A 40 kg slab rests on a frictionless floor. A 10 kg block rests on top of the slab (Fig. 6-58). The coefficient of static friction between the block and the slab is 0.60, whereas their kinetic friction coefficient is 0.40. The 10 kg block is pulled by a horizontal force with a magnitude of 100 N. What are the resulting accelerations of (a) the block and (b) the slab?

12. Example 5 Body A in Fig. weighs 102 N, and body B weighs 32 N. The coefficients of friction between A and the incline are and . Angle is 40°. Let the positive direction of an x axis be up the incline. In unit-vector notation, what is the acceleration of A if A is initially (a) at rest, (b) moving up the incline, and (c) moving down the incline?

13. Drag Force The magnitude of the drag force is related to the relative speed: • C is drag coefficient • ρ is the air density (mass per volume) • A is the effective cross-sectional area of the body (the area of a cross section taken perpendicular to the velocity ).

14. Terminal Speed When sky diving, a terminal speed will be reached when drag force is equal to the gravity.

15. Centripetal Force A centripetal force accelerates a body by changing the direction of the body’s velocity without changing the body’s speed. Important: a centripetal force is not a special type of force.

16. Sample Problem 6 In a 1901 circus performance, Allo “Dare Devil” Diavolo introduced the stunt of riding a bicycle in a loop-the-loop (Fig. 6-10a). Assuming that the loop is a circle with radius , what is the least speed v Diavolo could have at the top of the loop to remain in contact with it there?

17. Sample Problem 7 Curved portions of highways are always banked (tilted) to prevent cars from sliding off the highway. When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding. When the highway is wet, however, the frictional force may be negligible, and banking is then essential. Figure 6-13a represents a car of mass m as it moves at a constant speed v of 20 m/s around a banked circular track of radius R=190m . (It is a normal car, rather than a race car, which means any vertical force from the passing air is negligible.) If the frictional force from the track is negligible, what bank angle θ prevents sliding?

18. Conceptual Questions • Suppose that the coefficients of static and kinetic friction have values such that μs=2.0μk for a crate in contact with a cement floor. Does this mean that the magnitude of the static frictional force acting on the crate at rest would always be twice the magnitude of the kinetic frictional force acting on the moving crate? Give your reasoning. • A box rests on the floor of an elevator. Because of static friction, a force is required to start the box sliding across the floor when the elevator is (a) stationary, (b) accelerating upward, and (c) accelerating downward. Rank the forces required in these three situations in ascending order—that is, smallest first. Explain.

19. During the final stages of descent, a sky diver with an open parachute approaches the ground with a constant velocity. The wind does not blow him from side to side. Is the sky diver in equilibrium and, if so, what forces are responsible for the equilibrium?