Physics 20 Lesson 18 Pulleys and Systems

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1 Physics 20 Lesson 18 Pulleys and Systes I. Pulley and syste probles In this lesson we learn about dynaics probles that involve several asses that are connected and accelerating together. Using the pulley syste illustrated to the right below as an exaple, the basic ethod or solving probles involving a syste o asses is discussed. s in Lessons 15, 16 and 17, the basic ethod is to draw a ree body diagra o the orces involved, write an expression or the net orce, and then solve or the acceleration. 10 kg 5 kg In a pulley syste two asses are strung over a pulley. Note that downward acceleration or one o the asses results in upward acceleration or the other ass. hereore, when we assign directions to the orces acting on the asses we have to keep in ind that downward otion on one side o the pulley is equivalent to upward otion on the other side o the pulley. Most people choose () to be the direction that the syste will accelerate. In the exaple, thereore, down on the 10 kg side is () and 10 kg down on the 5 kg side is ( ). o calculate the acceleration o the asses, we note that the asses will accelerate at the sae rate together. I the asses accelerated at dierent rates, the string or rope between the asses would snap and there would no longer be a syste o asses. hereore, to calculate the acceleration we irst draw a ree body diagra or the syste as a whole. ro the ree body diagra we can write an expression or the net orce: NE g10 g5 We then use Newton s 2 nd law to calculate the acceleration o the syste NE a g10 g5 a 10 5 I you are asked to ind the tension in the rope or string, select one o the asses and draw the ree body diagra or the orces acting on that ass alone. (In our exaple I selected the 5 kg ass.) Note that the orces acting directly on the ass are and g5. g10 only acts on the 5 kg ass via the string or rope. ro the ree body diagra write the expression or NE. NE 5 g5 Since we have calculated the acceleration or the syste we can calculate NE 5 a NE 5 5 and then solve or the tension. NE 5 g5 g5 5 kg g5 5 kg 5 10 g10 Dr. Ron Licht

2 Exaple 1 30 kg ass is connected over a pulley with a 20 kg ass. What is the resulting acceleration when the asses are released? What is the tension in the rope? = 30 kg (9.81 /s 2 ) 30 kg = N 20 kg = 20 kg (9.81 /s 2 ) = N o calculate acceleration we draw the ree body diagra or the syste, write the net orce relationship and then use Newton s 2 nd law. g20 = N (syste) NE g30 g20 NE NE 294.3N 196.2N 98.1N NE a 98.1N a 30kg 20kg g30 = N a s o calculate the tension orce we choose one o the asses, draw the ree body diagra or the ass, write the net orce relationship, calculate the net orce, and then calculate the tension orce. I chose the 30 kg ass. 30 g30 NE 30 g30 NE 30 g N 294.3N 235N NE 30 NE 30 NE 30 a 30kg( 1.96 ) 58.9N 2 s 235N Dr. Ron Licht

3 Exaple kg ass rests on a surace which has a coeicient o riction o It is connected to a 100 kg ass over a pulley as shown in the diagra below. When the asses are released what is the resulting tension in the rope? 200 kg N 100 kg g100 = 100 kg (9.81 /s 2 ) = 981 N g200 = 200 kg (9.81 /s 2 ) = 1962 N syste N N g N 490.5N NE g100 NE NE Calculate tension. (I chose the 100 kg ass). g100 ro the ree body diagra or the syste note that the orce acting against is on the table 981N 490.5N 490.5N g100 NE a 490.5N a 100kg 200kg a s 100 g100 NE100 g100 NE100 g N 981N 817.5N NE100 NE100 NE100 a 100kg( ) 163.5N 2 s 818N Dr. Ron Licht

4 Exaple 3 or the syste below, ind the acceleration o the asses i the coeicient i riction is (10 kg) B (20 kg) 100 N N B N = 100 N = N = g10 = 0.12(98.1 N) = 11.8 N g10 = 10 kg (9.81 /s 2 ) = 98.1 N = N = g20 = 0.12(196 N) = 23.5 N g20 = 20 kg (9.81 /s 2 ) = N the ree body diagra or the syste is B 100 N NE = B NE = 11.8 N 23.5 N 100 N = 64.7 N NE 64.7N a = 2.16 /s 2 30kg Dr. Ron Licht

5 II. Practice probles kg ass is connected over a pulley to a 400 kg ass. What is the resulting acceleration when the asses are released? What is the tension in the rope? (1.96 /s 2, 4709 N) 400 kg 600 kg N orce is applied to a syste o asses. I ass has a 50 N rictional orce and ass B has a 70 N rictional orce, ind the acceleration o the syste. (0.60 /s 2 ) (20 kg) B (30 kg) Dr. Ron Licht

6 3. What is the acceleration and tension in the rope or the pulley syste shown i the coeicient o riction is 0.23? (0.76 /s 2, 9.05 N) 3.0 kg 1.0 kg Dr. Ron Licht

7 III. Hand-in assignent kg block on a level, rictionless table is connected to a 15 kg ass by a rope passing over a rictionless pulley. What will be the acceleration o the 15 kg ass when it is released? (2.7 /s 2 ) 40 kg 15 kg kg ass rests on a level rictionless table and is attached to a 3.0 kg ass by a light string that passes over a rictionless pulley. Calculate the tension in the string when the asses are released. (18 N) 5.0 kg 3.0 kg kg ass is attached to a 5.0 kg ass by a strong string that passes over a rictionless pulley. When the asses are released what will be (a) the acceleration o the asses, and (b) the agnitude o the tension in the string? (2.5 /s 2, 37 N) 3.0 kg 5.0 kg 4. In the diagra, ass is 100 kg and ass B is 25 kg and = What is the acceleration o ass and what is the tension in the rope? (0.392 /s 2, N) B 5. In the diagra, ass is 5.0 kg and ass B is 7.0 kg. What is the acceleration o the 5.0 kg ass and what is the tension in the rope? (1.64 /s 2, 57.2 N) B 6. wo girls, one o ass 40 kg and the other o ass 60 kg, are standing side by side in the iddle o a rozen pond. One pushes the other with a orce o 360 N or 0.10 s. he ice is essentially rictionless. (a) What is each girl's acceleration? (9.0 /s 2, -6.0 /s 2 ) (b) What velocity will each girl acquire in the 0.10 s that the orce is acting? (0.90 /s, /s) (c) How ar will each girl ove during the sae tie period? (4.5 c, -3.0 c) 7. ind the acceleration o asses and B i the coeicient o riction is (0.53 /s 2 ) (10 kg) B (20 kg) 60 N Dr. Ron Licht

8 8. Mr. Iron an Licht, weight = 883 N, and Mr. he an Christison, weight = 932 N, enjoy doing physics experients and oten ind theselves in odd situations. What is the resulting acceleration in each o the ollowing situations? a. he irst situation is where both Mr. L and Mr. C ind theselves dangling over a rictionless and weightless pulley syste. Mr. L Mr. C b. he second situation is where Mr. L is on the ground ( =.90) at the top o a cli and Mr. C is dangling over a rictionless and assless pulley syste over the cli. (What should Mr. L do?) Mr. L Mr. C c. he inal situation is where Mr. L is on a 60 o incline ( =.40) and Mr. C is dangling over a rictionless and assless pulley. Mr. L 60 o Mr. C Dr. Ron Licht

9 IV. Bonus questions 1. hree sall children o ass 20.0 kg, 24.0 kg, and 16.0 kg, respectively, hold hands, as shown, and are pulled across a sooth rozen pond by a larger boy on skates, who pulls a horizontal rope being held by the irst child. he skater pulls on the rope with a orce o 135 N. Calculate each o the ollowing. (a) the acceleration o the skater (2.25 /s 2 ) (b) the orce with which each pair o children ust hold hands, to ensure that the chain is not broken (90.0 N, 36.0 N) 2. In the diagra, ass is 170 kg. I the acceleration o the syste is 2.5 /s 2 towards B, what is the ass o B? (58.1 kg) B 3. In the diagra, ass is 5.0 kg. I the syste accelerates toward B at 4.0 /s 2, what is ass B? In addition, what is the tension in the rope? (11.9 kg, 69 N) B 4. I the coeicient o riction is 0.20, what is the acceleration o the syste? (1.6 /s 2 ) kg wooden block is placed on top o a 1.0 kg wooden block. he coeicient o static riction between the two blocks is he coeicient o kinetic riction between the lower block and the level table is What is the axiu horizontal orce that can be applied to the lower block without the upper block slipping? (8.1 N) 6. skier skiing downhill reaches the botto o a hollow with a velocity o 20 /s, and then coasts up a hill with a 10 o slope. I the coeicient o kinetic riction is 0.10, how ar up the slope will she travel beore she stops? (75 ) Dr. Ron Licht