Incline and Friction Examples
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- Miles Harrell
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1 Incline and riction Eample Phic 6A Prepared b Vince Zaccone
2 riction i a force that oppoe the motion of urface that are in contact with each other. We will conider 2 tpe of friction in thi cla: KINETIC riction for urface that are in motion (liding) STATIC riction for urface at ret Prepared b Vince Zaccone
3 riction i a force that oppoe the motion of urface that are in contact with each other. We will conider 2 tpe of friction in thi cla: KINETIC riction for urface that are in motion (liding) STATIC riction for urface at ret The formula are ver imilar each one ha a coefficient of friction (µ) that determine how much of the Normal force i tranlated into friction force. Crucial ditinction kinetic friction will be a contant force, while tatic friction will be jut trong enough to keep the urface from lipping Prepared b Vince Zaccone
4 riction i a force that oppoe the motion of urface that are in contact with each other. We will conider 2 tpe of friction in thi cla: KINETIC riction for urface that are in motion (liding) STATIC riction for urface at ret The formula are ver imilar each one ha a coefficient of friction (µ) that determine how much of the Normal force i tranlated into friction force. Crucial ditinction kinetic friction will be a contant force, while tatic friction will be jut trong enough to keep the urface from lipping Here are the formula: kinetic See friction i = µ N UN! k tatic µ N Static friction will have a maimum value. If ou puh an harder the urface will lip and ou get kinetic friction intead! Prepared b Vince Zaccone
5 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Prepared b Vince Zaccone
6 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force irt we draw a diagram of the force. friction puh weight Prepared b Vince Zaccone
7 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force irt we draw a diagram of the force. friction puh To get the bo moving we have to puh hard enough to overcome tatic friction. So we need to find the maimum force of tatic friction. tatic µ N weight Prepared b Vince Zaccone
8 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force irt we draw a diagram of the force. friction puh To get the bo moving we have to puh hard enough to overcome tatic friction. So we need to find the maimum force of tatic friction. tatic µ N weight The coefficient i given, but we need to find the normal force. We can ue the -direction force to find it. Prepared b Vince Zaccone
9 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force irt we draw a diagram of the force. friction puh To get the bo moving we have to puh hard enough to overcome tatic friction. So we need to find the maimum force of tatic friction. tatic µ N weight The coefficient i given, but we need to find the normal force. We can ue the -direction force to find it. Now we can calculate the maimum friction force. Σ = ma N mg= 0 N= mg N= ( 100kg)( 9.8 m) = 980N 2 Prepared b Vince Zaccone
10 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force irt we draw a diagram of the force. friction puh To get the bo moving we have to puh hard enough to overcome tatic friction. So we need to find the maimum force of tatic friction. tatic µ N weight The coefficient i given, but we need to find the normal force. We can ue the -direction force to find it. Now we can calculate the maimum friction force. ( 0.6) ( 980N) 588N tatic = Σ = ma N mg= 0 N= mg N= ( 100kg)( 9.8 m) = 980N 2 Prepared b Vince Zaccone
11 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force irt we draw a diagram of the force. friction puh To get the bo moving we have to puh hard enough to overcome tatic friction. So we need to find the maimum force of tatic friction. tatic µ N weight The coefficient i given, but we need to find the normal force. We can ue the -direction force to find it. Now we can calculate the maimum friction force. ( 0.6) ( 980N) 588N tatic = Σ = ma N mg= 0 N= mg N= ( 100kg)( 9.8 m) = 980N 2 Thi i how hard we have to puh to get the bo moving (ok, mabe we puh with a force of N) Now that we have the anwer for part a) how do we do part b)? Prepared b Vince Zaccone
12 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force Part b) i reall a kinematic problem. To find the anwer we need the acceleration of the bo. Then we can go back to chapter 2 and ue one of our kinematic formula. We can write down Newton 2 nd law for the -direction: Σ puh = ma friction= ma What tpe of friction do we have? friction weight puh Prepared b Vince Zaccone
13 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force Part b) i reall a kinematic problem. To find the anwer we need the acceleration of the bo. Then we can go back to chapter 2 and ue one of our kinematic formula. We can write down Newton 2 nd law for the -direction: Σ puh = ma friction= ma The bo i moving, o kinetic friction friction weight puh Prepared b Vince Zaccone
14 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force Part b) i reall a kinematic problem. To find the anwer we need the acceleration of the bo. Then we can go back to chapter 2 and ue one of our kinematic formula. We can write down Newton 2 nd law for the -direction: Σ puh puh = ma k friction= ma µ N= ma friction weight puh Prepared b Vince Zaccone
15 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force Part b) i reall a kinematic problem. To find the anwer we need the acceleration of the bo. Then we can go back to chapter 2 and ue one of our kinematic formula. We can write down Newton 2 nd law for the -direction: Σ = ma a puh puh k.98 friction= ma µ N= ma 588N (0.5) (980N) = (100kg) a m 2 friction weight puh Prepared b Vince Zaccone
16 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force Part b) i reall a kinematic problem. To find the anwer we need the acceleration of the bo. Then we can go back to chapter 2 and ue one of our kinematic formula. We can write down Newton 2 nd law for the -direction: Σ = ma puh friction= ma puh µ k N= ma 588N (0.5) (980N) = (100kg) a a m.98 2 friction weight puh Now that we have the acceleration we can ue our kinematic formula: = v 1 2 0, t+ a 2 t Prepared b Vince Zaccone
17 Eample puhing a bo acro the floor There i a 100kg bo at ret on a horizontal floor. The coefficient of friction are µ k =0.5 and µ =0.6. You want to puh it acro the room, o ou puh (horizontall) until it tart to lide. Once it tart to move, ou keep puhing with contant force. a) How hard do ou have to puh to get the bo moving? b) How far will the bo travel if ou puh for 3 econd? Normal force Part b) i reall a kinematic problem. To find the anwer we need the acceleration of the bo. Then we can go back to chapter 2 and ue one of our kinematic formula. We can write down Newton 2 nd law for the -direction: Σ = ma a puh puh k friction= ma µ 588N (0.5) (980N) = (100kg) a.98 N= ma m 2 friction weight puh Now that we have the acceleration we can ue our kinematic formula: = v 0, t+ 1 2 a = = 4.41m m 2 t 2 ( 3) 2 Prepared b Vince Zaccone
18 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. (ignore friction) Prepared b Vince Zaccone
19 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. (ignore friction) We can draw a diagram of force for thi problem. Siphu will puh up the incline, but the weight of the boulder will be traight down, o we will plit that one into component. Prepared b Vince Zaccone
20 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. (ignore friction) Normal Siphu We can draw a diagram of force for thi problem. Siphu will puh up the incline, but the weight of the boulder will be traight down, o we will plit that one into component. W boulder,downhill W boulder Prepared b Vince Zaccone
21 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. (ignore friction) Normal Siphu We can draw a diagram of force for thi problem. Siphu will puh up the incline, but the weight of the boulder will be traight down, o we will plit that one into component. or Siphu to be able to puh the boulder up the hill, hi force mut be at leat equal to the downhill component of the boulder weight. We can write down the formula like thi: W boulder,downhill = Siphu W boulder,downhill W boulder Prepared b Vince Zaccone
22 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. (ignore friction) Normal Siphu We can draw a diagram of force for thi problem. Siphu will puh up the incline, but the weight of the boulder will be traight down, o we will plit that one into component. or Siphu to be able to puh the boulder up the hill, hi force mut be at leat equal to the downhill component of the boulder weight. We can write down the formula like thi: W boulder,downhill W boulder W ( W ) ( in) W boulder,downhill boulder boulder = = in = Siphu Siphu Siphu Now all we need i Siphu How do we find that? Prepared b Vince Zaccone
23 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. (ignore friction) Normal Siphu We can draw a diagram of force for thi problem. Siphu will puh up the incline, but the weight of the boulder will be traight down, o we will plit that one into component. or Siphu to be able to puh the boulder up the hill, hi force mut be at leat equal to the downhill component of the boulder weight. We can write down the formula like thi: W ( W ) ( in) W boulder,downhill boulder boulder = = in = Siphu Siphu Siphu W boulder,downhill W boulder Siphu force can be found from the given information. He can lift 500kg, o multipling b g, hi force i 4900N. The angle i given a 20, o we can plug in to find our anwer. Prepared b Vince Zaccone
24 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. (ignore friction) Normal Siphu We can draw a diagram of force for thi problem. Siphu will puh up the incline, but the weight of the boulder will be traight down, o we will plit that one into component. or Siphu to be able to puh the boulder up the hill, hi force mut be at leat equal to the downhill component of the boulder weight. We can write down the formula like thi: W ( W ) ( in) W boulder,downhill boulder boulder = = in = Siphu Siphu Siphu W boulder,downhill W boulder Siphu force can be found from the given information. He can lift 500kg, o multipling b g, hi force i 4900N. The angle i given a 20, o we can plug in to find our anwer. 4900N W boulder = = 14,327N o in20 Prepared b Vince Zaccone
25 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Same a the lat problem, but now with added friction! Prepared b Vince Zaccone
26 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? Prepared b Vince Zaccone
27 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? DOWNHILL, oppoing Siphu. Notice that thi time we have labeled an ai tem with the - direction pointing uphill, and the -direction pointing directl awa from the incline. Thi wa we can write down two force formula. ƒ tatic W boulder, normal W boulder Siphu W boulder, Prepared b Vince Zaccone
28 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? DOWNHILL, oppoing Siphu. Notice that thi time we have labeled an ai tem with the - direction pointing uphill, and the -direction pointing directl awa from the incline. Thi wa we can write down two force formula. = ma = ma ƒ tatic W boulder, normal W boulder Siphu W boulder, Prepared b Vince Zaccone
29 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? DOWNHILL, oppoing Siphu. Notice that thi time we have labeled an ai tem with the - direction pointing uphill, and the -direction pointing directl awa from the incline. Thi wa we can write down two force formula. = ma = ma ƒ tatic W boulder, normal W boulder In thi tpe of problem we need all the force to balance out. Even though we want Siphu to be able to lift the boulder, we want to be jut on the borderline between when the boulder move and when it doen t. Thu we want to be in equilibrium to find the maimum weight. Equilibrium mean zero acceleration. Siphu W boulder, Prepared b Vince Zaccone
30 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? DOWNHILL, oppoing Siphu. Notice that thi time we have labeled an ai tem with the - direction pointing uphill, and the -direction pointing directl awa from the incline. Thi wa we can write down two force formula. ƒ tatic W boulder, normal W boulder Siphu W boulder, Prepared b Vince Zaccone
31 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? DOWNHILL, oppoing Siphu. Notice that thi time we have labeled an ai tem with the - direction pointing uphill, and the -direction pointing directl awa from the incline. Thi wa we can write down two force formula. Siphu f tatic Boulder, normal Boulder, ƒ tatic W boulder, normal W boulder Siphu W boulder, Prepared b Vince Zaccone
32 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? DOWNHILL, oppoing Siphu. Notice that thi time we have labeled an ai tem with the - direction pointing uphill, and the -direction pointing directl awa from the incline. Thi wa we can write down two force formula. Siphu f 4900N µ We are auming Siphu can puh with a maimum force of 4900 N. tatic normal Boulder, Boulder, normal normal = W Boulder, Boulder, ƒ tatic W boulder, normal W boulder Siphu W boulder, Prepared b Vince Zaccone
33 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? DOWNHILL, oppoing Siphu. Notice that thi time we have labeled an ai tem with the - direction pointing uphill, and the -direction pointing directl awa from the incline. Thi wa we can write down two force formula. Siphu f 4900N µ 4900N µ tatic normal normal Boulder, Boulder, Boulder in(20 ) o normal normal = W Boulder, Boulder ƒ tatic W boulder, co(20 o ) normal W boulder Siphu W boulder, Here where we ue our triangle Prepared b Vince Zaccone
34 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? DOWNHILL, oppoing Siphu. Notice that thi time we have labeled an ai tem with the - direction pointing uphill, and the -direction pointing directl awa from the incline. Thi wa we can write down two force formula. Siphu 4900N µ 4900N µ 4900N f tatic normal normal Boulder, in(20 ) o o ( 0.3) [ W co(20 )] in(20 ) Boulder Boulder, Boulder o Boulder normal normal = W Boulder, Boulder ƒ tatic W boulder, co(20 o ) normal W boulder Siphu W boulder, Now we can combine our equation b ubtituting for normal in the equation. We alo know the coefficient of friction. Prepared b Vince Zaccone
35 Siphu i attempting to puh thi giant boulder up an incline. Uing all hi trength he can lift 500kg traight up over hi head. If the incline i 20, find the maimum weight (in Newton) that Siphu can puh up the hill. Aume the coefficient of tatic friction i 0.3. Thi time we will have to include a friction force in our diagram. Which direction hould it point? DOWNHILL, oppoing Siphu. Notice that thi time we have labeled an ai tem with the - direction pointing uphill, and the -direction pointing directl awa from the incline. Thi wa we can write down two force formula. Siphu 4900N µ 4900N µ 4900N f tatic normal normal Boulder, o ( 0.3) [ W co(20 )] Boulder Boulder, Boulder in(20 ) o Boulder normal normal in(20 ) o = W Boulder, Boulder ƒ tatic W boulder, co(20 o ) normal W boulder Siphu W boulder, W Boulder = 7850N The final tep i jut a bit of algebra. Prepared b Vince Zaccone
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