Phyic 0 Leon 16 riction In the previou leon we learned that a rictional orce i any orce that reit, retard or ipede the otion o an object. In thi leon we will dicu how riction reult ro the contact between two urace. (Reer to Pearon pae 169 to 17, 176, and 180 to 184.) I. riction orce The current theory that decribe riction i quite coplicated and i beyond what we deal with in Phyic 0 and 30. However, or our purpoe, we will work with a iple (but reaonably accurate and ueul) approxiation o riction. When an object i in contact with a urace o oe kind (table, loor, paveent, concrete, etc.) there are two actor that deterine the rictional orce. The irt actor i the anitude (ize) o the noral orce actin on the object by the urace. The noral orce i actually the cobined eect o all the all orce o the urace actin on an object. object The noral orce i the u o all the all orce o contact. urace The reater the noral orce, the reater the interaction between the ato and electron o the object and the urace and, thereore, the reater the rictional orce. The econd actor i the nature o the interaction between object and the urace. I the urace and object are rouh in texture, like coare andpaper on bruhed concrete, the rictional orce will be quite dierent copared to the interaction between ine andpaper and ooth concrete. In addition, there i the interaction between the ato and electron o the object and the ato and electron o the urace. The interaction between a rubber tire and a dry paveent urace, or exaple, i ubtantially dierent ro the interaction between a rubber tire and an icy urace. The interaction between the urace i repreented by a nuber (pronounced u ) called the coeicient o riction. The coeicient o riction can be thouht o a an indicator o the tickine o the interaction between two urace the hiher the coeicient, the tickier the interaction, the reater the rictional orce. or rictionle interaction, which are only theoretical, = 0. In the table below a nuber o coeicient are iven (ee Pearon pae 183 a well). ote that the coeicient o riction i unitle. Surace wood on wood waxed wood on now etal on etal with oil rubber on olid huan hip joint Coeicient o tatic riction, 0.40 0.14 0.15 1 to 4 <0.01 Coeicient o kinetic riction, k 0.0 0.10 0.07 1 <0.01 Dr. Ron Licht 16-1 www.tructuredindependentlearnin.co
ote that there are two type o rictional coeicient and k. The coeicient o tatic riction ( ) i ued to calculate the rictional orce between object that are not lidin relative to one another. The tatic rictional orce ut be overcoe to tart the object lidin. The kinetic coeicient o riction ( k ) i ued to calculate the rictional orce when an object i already lidin over a urace. The two actor, noral orce and coeicient o riction, cobine to ive the ollowin equation: 50k(9.81 ) 490.5 ote the abolute value ybol they ean that we are reerrin to the anitude o the orce and not their direction. Exaple 1 What riction orce ut be overcoe to tart a 50 k object lidin acro a horizontal urace when the tatic coeicient o riction i 0.35? Exaple ro the diara, 490.5 A 400 object i pulled over a horizontal urace. I the coeicient o kinetic riction i 0.3 and the applied orce i 10, what i it acceleration? = 10 ro the diara, 400 0.35(490.5) Calculate the rictional orce 0.3(400) 9 1.7 10 Calculate the a ro 400 9.81 40.77k ro the ree body diara ET A 10 ( 9) ET ET 8 Calculate the acceleration ET a 8 a 40.77k a 0.69 Dr. Ron Licht 16 - www.tructuredindependentlearnin.co
Exaple 3 A 10 k box i draed over a horizontal urace by a orce o 40. I the box ove with a contant peed o 0.5 /, what i the coeicient o kinetic riction or the urace? ro the vector diara ET A v i contant 0 ET 0 40 40 10k(9.81 ) 98.1 40 98.1 0.41 Exaple 4 A 10 k box i draed acro a level loor with a orce o 60. The orce i applied at an anle o 30 above the horizontal. I the coeicient o riction i 0.0, what i the acceleration o the box? 60 30 o ote that oe o the applied orce i pullin the box and oe i litin the box. Due to the litin orce, there i a aller noral orce actin on the block. Thereore the aount o riction will decreae. Breakin the applied orce into it coponent: = = 10 k(9.81 / ) = 98.1 30 o Ax = 60 co 30 o Ax = 51.96 Ay = 60 in 30 o Ay = 30 In the vertical dienion ET(V) Ay 0 30 98.1 68.1 0.0(68.1) 13.6 Since the object doe not ove up or down ET (V) = 0 In the horizontal dienion ET(H) Ax ET(H) ET(H) 51.96 13.6 38.34 Calculate acceleration ET a 38.34 a 10k a 3.83 Dr. Ron Licht 16-3 www.tructuredindependentlearnin.co
II. Practice proble 1. A 15 k box i bein draed over a concrete loor with an applied horizontal orce o 40. I the coeicient o kinetic riction i 0.5, what i the acceleration o the box? (0.1 / ). A 0 k apple crate i bein draed acro a loor at contant velocity with a horizontal orce o 5. What i the coeicient o riction? (0.13) 3. A rope attached to a 50 k box i bein pulled at an anle o 5 o acro a horizontal loor where the coeicient o tatic riction i 0.0. What i the acceleration o the box i a 00 orce i applied? (.1 / ) Dr. Ron Licht 16-4 www.tructuredindependentlearnin.co
III. Hand-in ainent 1. or each ituation below, draw accurate ree-body diara howin all orce actin on the rock. A. Slidin at contant peed without riction. B. Deceleratin becaue o kinetic riction.. It take a 50 horizontal orce to pull a 0 k object alon the round at contant velocity. What i the coeicient o riction? (0.6) 3. I the coeicient o riction i 0.30, how uch horizontal orce i needed to pull a a o 15 k acro a level board with contant velocity? (44 ) 4. A box, a =.0 k, i pulled acro a level dek by a horizontal orce o 4.0. I the coeicient o kinetic riction i 0.1, what i the acceleration o the box? (0.83 / ) 5. A irl puhe a liht (i.e. weiht i neliible) now hovel at a unior velocity acro a idewalk. I the handle o the hovel i inclined at 55 o to the horizontal and he puhe alon the handle with a orce o 100, what i the orce o riction? What i the coeicient o kinetic riction? (57, 0.70) 6. A 70 k hockey player coat alon the ice on teel kate. I the coeicient o kinetic riction i 0.010, (a) what i the orce o riction? (b) How lon will it take hi to coat to a top, i he i initially travellin at 1.0 /? (6.9, 10 ) 7. A 10 k box i pulled acro a level loor, where the coeicient o kinetic riction i 0.35. What horizontal orce i required or an acceleration o.0 /? (54 ) 8. A boy pull a 50 k crate acro a level loor with a orce o 00. I the orce act at an anle o 30 o up ro the horizontal, and the coeicient o kinetic riction i 0.30, deterine (a) the noral orce exerted on the crate by the loor, (3.9 x 10 ) (b) the rictional orce exerted on the crate by the loor, (1. x 10 ) (c) the acceleration o the crate. (1.1 / ) 9. A can o pop (a = 500 ) i iven a hove. It lide acro a table, eventually coin to a top. I it initial velocity i.0 /, and the coeicient o kinetic riction between the two urace i 0.0, how ar will it travel acro the table? (1.0 ) Dr. Ron Licht 16-5 www.tructuredindependentlearnin.co
Coeicient o riction Activity Purpoe: To eaure the kinetic coeicient o riction or a urace. Material: wood block with trin ae ro 0.10 k to 1.0 k raph paper prin balance thinkin tudent() Analyi: Rearranin the riction equation = we have rie lope run Thu i we plot a raph o V and calculate the lope o the bet-it-line, the lope will equal the coeicient o riction (). Make ure the axi on your raph atch the equation. Procedure: 1. Chooe a uitable wooden block. The a i written on the block.. Contruct a data table like the one below a a part o your write-up. 3. Place the irt a on the block. Calculate the weiht o the total a. Wooden block 4. Dra the block and a acro the urace akin ure to pull horizontally and at a contant peed. The prin cale readin i the applied orce. 5. Repeat tep 3 to 4 or the other ae. 6. On a heet o raph paper draw a raph or the data. 7. Calculate the lope o the line-o-bet-it or the raph. Data Table: Extra a Weihin cale Applied orce Extra Ma (k) 0.60 Total Ma (k) () () A () kinetic () kinetic 0.80 1.00 1.0 1.40 1.60 Dr. Ron Licht 16-6 www.tructuredindependentlearnin.co
Analyi and Interpretation: 1. Draw a ree-body diara o the block with an applied orce jut beore it tart to ove.. Draw a ree-body diara o the block a it i bein pulled acro a urace at contant peed. 3. Explain why the applied orce hould be applied horizontally and not at an anle. 4. Explain why the block hould be pulled at a contant peed. 5. What i the relationhip between the applied orce and the rictional orce? 6. What i the relationhip between weiht and the noral orce? 7. What i the unit or the coeicient o riction? Do your calculation how thi? Write-up: data and obervation raph calculation anwer to Analyi and Interpretation Dr. Ron Licht 16-7 www.tructuredindependentlearnin.co