LECTURE 9 FRICTION & SPRINGS. Instructor: Kazumi Tolich

Transcription

1 LECTURE 9 FRICTION & SPRINGS Instructor: Kazumi Tolich

2 Lecture 9 2 Reading chapter 6-1 to 6-2 Friction n Static friction n Kinetic friction Springs

3 Static friction 3 Static friction is the frictional force that prevents surfaces in contact from sliding. F The direction of the static friction is anti-parallel to all the other forces trying to slide the object relative to the surface. While the object is not sliding on a surface, the magnitude of the static friction equals the magnitude of all the other forces trying to slide the object until it reaches the maximum value. N f $ 0 f $ f $,&'( = μ $ N f $ F μ $ is the coefficient of static friction (dimensionless). N is the magnitude of the normal force by one surface on the other. FBD of the block W

4 Quiz: 1 A box sits on the horizontal bed of a moving truck. As the truck accelerates to the left, the box does not slide on the truck bed. Does the truck bed exerts static friction on the box? If so, what is the direction of this static friction on the box? A. No. The truck bed does not exert any static friction on the box. B. Yes. The truck bed exerts static friction on the box to the right. C. Yes. The truck bed exerts static friction on the box to the left.

5 Quiz: 9-1 answer Yes. The truck bed exerts static friction on the box to the left. The box is accelerating to the left with the truck. So, there must be a net force on the box to the left. That leftward force must be the static friction by the truck bed.

6 Quiz: 2 A block is placed on a rough incline. A force F is applied up the incline just enough to prevent the block from sliding down. Draw a force vector representing the direction of the friction in the figure. F

7 Quiz: 9-2 answer up along the incline A force F is applied up the incline just enough to prevent the block from sliding down, so if F was slightly smaller, the block would be sliding down. The static friction is preventing the block from sliding down. f $

8 Quiz: 3 8 A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? Choose all that apply. A. Component of the gravity force parallel to the plane increased. B. Coefficient of static friction decreased. C. Normal force exerted by the board decreased.

9 Quiz: 9-3 answer 9 A. Component of the gravity force parallel to the plane increased. B. Coefficient of static friction decreased. C. Normal force exerted by the board decreased. As the angle θ increases, the component of weight parallel to the plane (W sin θ) increases and the component perpendicular to the plane (W cos θ) decreases. When the box is not sliding, F = 0. So N = W cos θ and f $ = W sin θ. As θ increases, N decreases, and f $ increases. However, f $,&'( = μ $ N, we see that f $ reaches the maximum, while the force pulling the box down the plane gets bigger. N ;< f $ ;< θ θ W ;=

10 Example: 1 10 A crate with a mass of m = 45 kg is placed on an inclined ramp. When the angle the ramp makes with the horizontal is increased to θ = 23º, the crate begins to slide downward. What is the coefficient of static friction between the crate and the ramp?

11 Demo: 1 11 Four surface incline Demonstration of various materials with different coefficients of static friction Incline with Sliding Blocks (with Tacky Wax) Demonstration of various surfaces with different coefficients of static friction. Coefficient of static friction can be measured by the maximum angle without the block sliding. N ;< f $ ;< θ μ $ = tan θ θ W ;=

12 Kinetic friction 12 Kinetic friction is the frictional force that opposes sliding motion. The direction of the kinetic friction is anti-parallel to the velocity of the sliding object relative to the surface. The magnitude of the kinetic friction is given by f A = μ A N μ A is the coefficient of kinetic friction (dimensionless). N is the magnitude of the normal force by one surface on the other.

13 Quiz: 4 13 Four identical blocks labeled 1 through 4 as shown are moving on a surface for which the coefficient of kinetic friction between each block and the surface is µ k. The velocity of each block is indicated by the vector on the block. Rank the blocks according the magnitudes of the frictional force on the blocks, smallest first.

14 Quiz: 9-4 answer 14 1 = 2 = 3 = 4 Kinetic friction is independent of the relative speed of the surfaces or the area of contact between the surfaces.

15 Demo: 2 15 Contact area and kinetic friction

16 Example: 2 16 A hockey puck with a mass m = 0.11 kg whose initial speed was v CD = 6.0 m/s slides on the ice for x = 15.0 m before it stops. a) What was the magnitude of the frictional force on the puck during the sliding? b) What was the coefficient of friction between the puck and the ice?

17 Reducing frictions in bodies 17 Joints Many parts of the body, especially the joints, have coefficients of friction that are three or four times less than those of ice. The joints are covered by cartilage, which provides a smooth, almost glassy surface. The joints also produce a lubricating fluid. A damaged joint can be replaced by an artificial joint made of metals (stainless steel or titanium) or plastic (polyethylene) with very small coefficients of friction. Swallowing knee joint replacement Saliva acts like a lubricant and helps you to swallow.

18 Spring force 18 Force exerted by a compressed or stretched spring obeys Hook s law. F D = kx : the direction of the force is opposite from the displacement of the end of the spring. This type of force is called restoring force. k: force constant for stiffness of the spring. x: the displacement of the end of the spring.

19 Demo: 3 19 Hook s Law

20 Example: 3 20 A backpack weighing W = 52.0 N rests on a table. A spring with a force constant of k = 150 N/m is attached to the backpack and pulled horizontally. If the spring is pulled until it stretches x = 2.00 cm and the pack remains at rest, what is the force of friction exerted on the backpack by the table?