LECTURE 11 FRICTION AND DRAG

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1 LECTURE 11 FRICTION AND DRAG 5.5 Friction Static friction Kinetic friction 5.6 Drag Terminal speed Penguins travel on ice for miles by sliding on ice, made possible by small frictional force between their bellies and ice.

2 Learning objectives 2! Distinguish between static and kinetic frictions.! Use the simple model of frictions! 0 # $ # $ %&' = ) $ *! # + = ) $ *! Calculate and deduce the magnitude and direction of a frictional force in a given situation.! Calculate the coefficient of static friction from the maximum angle of an incline.! Calculate and deduce the magnitude and direction of drag force given the velocity and the dimension of an object.! Calculate the terminal speed of a falling object.

3 5.5 Static friction! The static friction force has a maximum possible magnitude: 0 # $ # $ %&' = ) $ * where ) $ is the coefficient of static friction.

4 Quiz: 5.5-1! A block is placed on a rough incline. A force " 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. "

5 Quiz: answer! up along the incline! To find the direction of static friction, decide which way the object would move if there were no friction. The static friction force then points in the opposite direction.! While the component of the weight of the object tries to slide down the object, the force " is applied up the incline just enough to prevent the block from sliding down, so if there was no friction, the block would be sliding down.! The static friction is up the incline, preventing the block from sliding down. # +) " () * +), -),0, -), -),/ & % # $

6 5.5 Kinetic friction! Kinetic friction has a nearly constant magnitude given by where $ " is the coefficient of kinetic friction.! " = $ " %

7 Quiz: ! A block rests on a table where the coefficients of static and kinetic friction between the table and the block, respectively, are! " and! #. The block is pulled by a rope with slowly increasing tension, $. The magnitude of the friction between the block and the table is % and the magnitude of the normal force on the block is &. Select all the statements that are correct. A. While the block is stationary % = $. B. While the block is stationary % =! " &. C. While the block is moving % = $. D. While the block is moving % =! # &. E. The block starts moving with any $ greater than zero. F. The block starts moving only once $ is large enough.

8 Quiz: answer / demo 8! Select all the statements that are correct A. While the block is stationary! = #. B. While the block is stationary! = $ % &. C. While the block is moving! = #. D. While the block is moving! = $ ' &. E. The block starts moving with any # greater than zero. F. The block starts moving only once # is large enough.! % = #! % ()* = $ % &! ' = $ ' & &,- # # 0-!,- Block starts moving when # is this big. /-

9 Group exercise:! "! $ 9! You have to push harder to get an object to begin sliding than to keep it sliding at constant speed.! Discuss why for any given contacting surfaces,! "! $.! If! " >! $, what would happen just as an object starts sliding?

10 Group exercise:! "! $ answer 10! You have to push harder to get an object to begin sliding than to keep it sliding at constant speed.! Discuss why for any given contacting surfaces,! "! $.! If! " >! $, what would happen just as an object starts sliding?! After you reach the maximum tension for the block to remain stationary, if you then increased the tension an infinitesimal amount, the block will start sliding.! But if! " >! $, the friction would increase, so the net force on the block would be in the direction of the friction and the block would stop sliding as the force is in the opposite direction to the motion. If#! " >! $ & $,() =! $ + () + (). /), -) Just before starting sliding + (). /) 1 & ",() =! " + (), -) Just after starting sliding

11 Friction in human joints 11! 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. Table 5.1 Coefficients of Static and Kinetic Friction System Static friction μ s Kinetic friction μ k Rubber on dry concrete Rubber on wet concrete Wood on wood Waxed wood on wet snow Metal on wood Steel on steel (dry) Steel on steel (oiled) Teflon on steel Bone lubricated by synovial fluid Shoes on wood Shoes on ice Ice on ice Steel on ice knee joint replacement

12 Group exercise: box on a ramp 12! A box sits on a flat plank that makes an angle of! from a flat floor. Draw a free-body diagram of the box.

13 Group exercise: box on a ramp answer 13 ) *+ / "+ sin (, -,*+! $ "# cos ( / "+ / "+ cos (

14 Question ! A box sits on a flat plank on a floor. You lift one end of the plank, 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. The component of the gravitational force on the box parallel to the plank increased. B. The normal force exerted by the plank on the box decreased. C. The coefficient of static friction decreased.

15 Quiz: answer 15 A. The component of the gravity force parallel to the plank increased. B. The normal force exerted by the plank decreased. C. The coefficient of static friction decreased.! As the angle! increases, the component of weight parallel to the plank (" #$ sin!) increases and the component perpendicular to the plank (" #$ cos!) decreases.! When the box is not sliding,, = 0. So / 0$ = " #$ cos! and 1 2,0$ = " #$ sin!.! As! increases, / 0$ decreases, and 1 2,0$ increases.! However, 1 2,456,0$ = 7 2 / 0$, so we see that 1 2,0$ reaches the maximum, while the force pulling the box down the plank gets bigger. " #$ sin! / 0$ = " #$ cos! 1 :,0$ = " #$ sin!, 9 #8 cos! " #$ " #$ cos!

16 Quiz: ! A box is placed on an inclined plank. When the angle the plank makes with the horizontal is increased to! "#$ = 30º, the box begins to slide downward. What is the coefficient of static friction between the box and the plank? -./ = 0 '/ cos! 0 '/ sin! 1 2,./ = 0 '/ sin! & ) '( cos! 0 '/ 0 '/ cos!

17 Quiz: answer / demo 17! A box is placed on an inclined plank. When the angle the plank makes with the horizontal is increased to! "#$ = 30º, the box begins to slide downward. What is the coefficient of static friction between the box and the plank?! & ',"#$,)* = + ', )*! -.* sin! "#$ = + ' -.* cos! "#$! + ' = tan! "#$ = tan 30 = 0.58! Demo: Incline with Sliding Blocks -.* sin!, )* = -.* cos! &?,)* = -.* sin! < >.= cos! -.* -.* cos!

18 Quiz: Kinetic friction and surface area 18! Three identical blocks labeled 1 through 3 are pulled across a flat surface at the velocities shown. Rank the magnitudes of the frictional force on the blocks from smallest to largest.! 3 2! 2! 1

19 Quiz: Kinetic friction and surface area answer / demo 19! Three identical blocks labeled 1 through 3 are pulled across a flat surface at the velocities shown. Rank the magnitudes of the frictional force on the blocks from smallest to largest.! 1=2=3! Kinetic friction only depends on the normal force, not on the contact area or the speed.! 3 2! 2! 1

20 5.6 Drag! In our everyday experience, the drag force can be modeled as! = # $ % &'() $ # + '()$! Here, ' = 1.2 kg m 3 is the density of air at sea level, ( is the crosssection area of the object, ) is the speed of the object, and the drag coefficient % &, whose value for everyday moving objects is roughly ½.

21 5.6 Terminal speed / demo! The speed at which the exact balance between the upward drag force and the downward weight force causes an object to fall without acceleration is called the terminal speed.! HOW CAN A CAT SURVIVE A HIGH-RISE FALL? PHYSICS!!