Laws of Motion Friction More Problem Solving

Transcription

1 Laws of Motion riction More Problem olving Lana heridan De Anza College Oct 16, 2017

2 Last time elevators pulleys

3 Overview riction Problem solving with forces

4 Pulleys and the Atwood Machine The Atwood Machine can be used to make careful determinations of g, as well as explore the behavior of forces and accelerations. nless pulley of twood machine. lue of g. Detertension in the + T T action: as one se the objects st be of equal e gravitational em. Therefore, a m 1 m 2 + m 1 m 1 g 1 machine b m 2 m 2 g

5 Pulleys and the Atwood Machine y-direction: Take eq (1) + eq (2): up +ve: net,y,1 = T m 1 g = m 1 a (1) down +ve: net,y,2 = m 2 g T = m 2 a (2) m 2 g m 1 g = m 1 a + m 2 a a = (m 2 m 1 )g m 1 + m 2

6 Pulleys and the Atwood Machine y-direction: Take eq (1) + eq (2): up +ve: net,y,1 = T m 1 g = m 1 a (1) down +ve: net,y,2 = m 2 g T = m 2 a (2) m 2 g m 1 g = m 1 a + m 2 a a = (m 2 m 1 )g m 1 + m 2 T = 2m 1m 2 g m 1 + m 2

7 riction friction The force caused by small-scale roughness of surfaces or even electrostatic attractions between surfaces. It dissipates energy and resists motion. Kinetic friction is the friction force that acts on moving objects. It is given by: kf = µ k n = µ k n tatic friction is the friction force that acts on objects that are at rest: sf µ s n sf (max) sf (max) sf = µ s n

8 riction friction equals the magnitude of the applied force. static friction, the trash can breaks free and accelerates to the right. n n Motion fs fk mg mg a f b f s,max f s f k m k n O tatic region Kinetic region c

9 riction Example According to the textbook, for waxed wood on wet snow µ s = 0.14 and µ k = 0.1. You pull on a sled of mass 10 kg that is at rest initially. How much force do you need to apply to get the sled moving? If you continue to apply that force, what will the magnitude of sled s acceleration be once it is moving?

10 riction Question Quick Quiz You are playing with your daughter in the snow. he sits on a sled and asks you to slide her across a flat, horizontal field. You have a choice of: (A) pushing her from behind by applying a force downward on her shoulders at 30 below the horizontal or (B) attaching a rope to the front of the sled and pulling with a force at 30 above the horizontal. Which would be easier for you and why? 2 erway & Jewett, page 132. a b igure 5.17 (Quick Quiz 5.7) A father slides his daughter on a sled either by (a) pushing down on her shoulders or (b) pulling up on a rope. Rubb tee Alum Glas Cop Woo Wax Wax Meta Teflo Ice o yno Note: can e Q u yo b Q u a ch sh th (

11 ome More orce Problems We already considered many different situations where we could analyze forces to determine motion. Now, we can mix some of those situations into more complex cases.

12 er from behind by applying a force downward on her the Incline horizontal with (ig. riction 5.17a) or (b) attaching a rope to d pulling with a force at 30 above the horizontal ld be easier for you and why? Given a block of mass m = 1 kg on an incline of θ = 30 with a M coefficient of static friction of µ s = 0.3, will the block slide? s and M k AM ts of friction. uppose e horizontal as shown k starts to move. how hich this slipping just e block tends to slide te the situation, place begins to slide. Notice is no friction on an ject to begin moving. e object for angles less fs mg cos u u mg n y mg sin u igure 5.18 (Example 5.11) The external forces exerted on a block lying on a rough incline are the gravitational force mg, the normal force n, and the force of friction fs. or convenience, the gravitational force u x

13 Incline with riction AM nation of M s and M k coefficients of friction. uppose lative to the horizontal as shown til the block starts to move. how angle u c at which this slipping just ne that the block tends to slide. To simulate the situation, place il the coin begins to slide. Notice hen there is no friction on an tionary object to begin moving. ment of the object for angles less ces. Because we are raising the y to begin to move but is not movrium. rces on the block: the gravitational force mg, the normal force n, and parallel to the plane and y perpendicular to it. quation 5.8 (1) o x 5 mg sin u 2 f s 5 0 (2) o y 5 n 2 mg cos u 5 0 fs mg cos u u mg n y mg sin u igure 5.18 (Example 5.11) The external forces exerted on a block lying on a rough incline are the gravitational force mg, the normal force n, and the force of friction fs. or convenience, the gravitational force is resolved into a component mg sin u along the incline and a component mg cos u perpendicular to the incline. If the net force is not zero, it will be downward parallel to the slope. u x

14 nalysis Models Using Newton s econd Law 129 Pulley with an Incline ected by a Cord Let s change up our Atwood machine apparatus so that one of the masses is on a slanted surface with no friction: y tweight cord igure 5.15a. agnitude of. a m 1 AM m 2 a u T m 1 x g If m 2 moves cts are conccelerations a n y b

15 jects Pulley Connected with an by Incline a Cord AM 5.7 Analysis Models Using Newton s econd Law y 129 hed by a lightweight cord e mass as in igure 5.15a. cceleration of Two Objects Connected by a Cord AM u. ind the magnitude of m T 2 y n block in the of mass cord. m 2 are attached by a lightweight cord x m ionless pulley of negligible mass as in a igure a. a m 1 g ictionless d Law incline of angle u. 129 ind the magnitude of u m T 2 two objects and the tension in the cord. x 5 in motion. If m 2 moves a u b use the Weobjects can still are consider conetch), the objects their in accelerations igure 5.15 in motion. If m 2 moves a b each object separately: y e n m n oordinate 1 moves upward. Because axes in y the objects are conch we assume does not stretch), their accelerations y igure ck in igure 5.15c. T n ude. Notice the normal coordinate axes in igure he tilted axes for the block e two objects and we are m 2 g sin u T in igure 5.15c. T entify objects forces as on particles each of under the two a objects and we are m 2 g sin u tion, so we categorize the objects the x9 direction. In the y9 2 g cos u x x as particles m under ua u x this model is only valid for the x9 direction. In the y9 m2g cos u el particle because in equilibrium the block model mdoes 1 gbecause the block does m 2 g m 2 g irection. c c Acceleration? Tension? free-body diagrams shown in igures 5.15b and n in igures 5.15b and igure 5.15 (Example 5.10) (a) Two objects a m 1 m 1 g

16 Pulley with an Incline Acceleration? (A) a = (m 2 sin θ m 1 )m 1 g m 1 +m 2 (B) a = (m 2 sin θ m 1 )g m 1 +m 2 (C) a = (m 2 sin θ)g m 1 +m 2 (D) None of the above. + g Tension? (A) T = m 1m 2 (sin θ+1)g m 1 +m 2 (B) T = m2 2 (sin θ+1)g m 1 +m 2 (C) T = (m 2 sin θ m 1 )g m 1 +m 2 (D) None of the above. m 1 g

17 Pulley with an Incline

18 Pulley with an Incline

19 ne the sumed emergency, what is the minimum time interval in which a person starting from rest can move 3.00 m on the tile surface if she is wearing (a) footwear meeting the Postal ervice minimum and (b) a typical athletic shoe? Tension and orce: #60, pg 144 izontal tween minihat is d m s 5 al surto set rce of h conriction en the.80-kg tal seat en the kinetic km/h over a 60. A woman at an airport is towing W her 20.0-kg suitcase at constant speed by pulling on a strap at an angle u above the horizontal (ig. P5.60). he pulls on the u strap with a 35.0-N force, and the friction force on the suitcase is 20.0 N. (a) Draw a freebody diagram of the suitcase. igure P5.60 (b) What angle does the strap make with the horizontal? (c) What is the magnitude of the normal force that the ground exerts on the suitcase? 61. Review. A 3.00-kg block starts from rest at the top of a M 30.0 incline and slides a distance of 2.00 m down the incline in 1.50 s. ind (a) the magnitude of the acceleration of the block, (b) the coefficient of kinetic friction

20 Pulley ystem: #85, page 147 move, determine (d) the sum of the magnitudes of the forces of friction acting on the blocks. 85. An object of mass M is held in place by an applied force and a pulley system as shown in igure P5.85. The pulleys are massless and frictionless. (a) Draw diagrams showing the forces on each pulley. ind (b) the tension in each section of rope, T 1, T 2, T 3, T 4, and T 5 and (c) the magnitude of. 86. Any device that allows you to increase the force you exert is a kind of machine. T 1 T 4 T 2 T 3 M T 5 igure P5.85

21 choose the x direction as u north of east and the y direction as u west of north. (c) Compare Tension and your orce solutions Meters: to parts (a) and #28, (b). Do the page results agree? 141 Is one method significantly easier? 28. The systems shown in igure P5.28 are in equilibrium. W If the spring scales are calibrated in newtons, what do they read? Ignore the masses of the pulleys and strings and assume the pulleys and the incline in igure P5.28d are frictionless kg a 5.00 kg 5.00 kg b t s. 33. A bag of cemen AMT hangs in eq W three wires as ure P5.33. Two angles u with the horiz the system is find the tensio in the wires. 34. A bag of ceme is g hangs in e three wires as P5.33. Two of angles u 1 and u tem is in equili hand wire is c 5.00 kg kg 5.00 kg d igure P Two people pu ropes attached If they pull in acceleration of opposite direc m/s 2 to t force each per other horizonta

22 are set into motion when is applied.) (b) How does liding the Blocks 8.00-kg with block riction: move #103, in the page process? 149 igure P5.103 m M L a M m b

23 shown in the figure and then slides down again, liding Blocks always without with friction. riction: ind #103, the force page that the 149 tabletop exerts on the incline throughout this motion in terms of m, M, g, and u. ster tion p is essly has and 0 N. sucthe 103. A block of mass m kg rests on the left edge of a block of mass M kg. The coefficient of kinetic friction between the two blocks is 0.300, and the surface on which the 8.00-kg block rests is frictionless. A constant horizontal force of Problems magnitude N is applied to the 2.00-kg block, setting it in motion as shown in igure P5.103a. If the distance L that the leading edge of the smaller block travels on the larger block is 3.00 m, (a) in what time interval will the smaller block make it to the right side of the 8.00-kg block as shown in igure P5.103b? (Note: Both blocks are set into motion when is applied.) (b) How far does the 8.00-kg block move in the process? m M L

24 102. In igure P5.101, the incline has mass M and is fas- tened to the stationary horizontal tabletop. The block liding Blocks with riction: #103, page 149 of mass m is placed near the bottom of the incline and Problems 149 is released with a quick push that sets it sliding upward. The block stops near the top of the incline as shown in igure P5.103a. If the distance L that the shown in the figure and then slides down again, leading edge of the smaller block travels on the larger always without friction. ind the force that the tableblock is 3.00 m, (a) in what time interval will the smaller block make it to the right side of the 8.00-kgtop exerts on the incline throughout this motion in block as shown in igure P5.103b? (Note: Both blocksterms of m, M, g, and u. fara block of mass m kg rests on the left edge of a are set into motion when is applied.) (b) How 103. does the 8.00-kg block move in the process? block of mass M kg. The coefficient of kinetic friction between the two blocks is 0.300, and the surl face on which the 8.00-kg block rests is frictionless. A m constant horizontal force of Problems magnitude N is M applied to the 2.00-kg block, setting it in motion as lowing situation impossible? A 1.30-kg toaster shown in igure P5.103a. If the distance L that the a ged in. The coefficient of static friction leading edge of the smaller block travels on the larger m e toaster and a horizontal countertop is block is 3.00 m, (a) in what time interval will the M you carelessly ake the toaster start moving, smaller block make it to the right side of the 8.00-kg electric cord. Unfortunately, the cord has block as shown in igure P5.103b? (Note: Both blocks b yed from your previous similar actions and are set into motion when is applied.) (b) How far does the 8.00-kg block move in the process? f the tension in the cord exceeds 4.00 N. igure P5.103 on the cord at a particular angle, you sucl rta the toaster movingbywithout breaking the buttermobile is formed supporting four metal flies of equal mass m from a string of length L. The points support evenly a distance lock ofofmass m 5are 2.00 kg isspaced released from, apart as shown in igure P of The string at forms m above the surface a table, the an angle with incline the ceiling at eachinendpoint. The center sec5u130.0 as shown igure P tion of string is horizontal. (a) ind the tension in nless incline is fixed on a table of height each section of string in terms of u1, m, and g. (b) In m. (a) Determine the acceleration of the terms of u, find the angle u that the sections of string m M a M m

25 ummary friction more practice with force problems (Uncollected) Homework erway & Jewett, Work through Example 5.13 on page 134 and understand it. Ch 5, onward from page 136. Obj.Q 1; Problems: 45, 65, 89, 93, 101