UNIT 4 READING B. net y. net x

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Derick Phelps
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1 UIT 4 READI B rce Diagrams Yu have learned in lab abut ur dierent tpes rces nrmal, gravitatin, tensile, and rictinal. In this class, rce diagrams will be drawn as llws: 1) The bject n which the rces are acting will be represented b a dt. 2) The rces will be drawn as arrws pinting in the directin the rce, with the tail the arrw n the dt. 3) Each rce shuld be labeled: r each rce, the tpe rce shuld be indicated and it shuld be clear which bject is eerting the rce. In ur stud kinematics, we und that the equatins mtin can be applied independentl t the - and - directins. Similarl, the - and - cmpnents rces are independent each ther. S the equatin = ma, can be written as tw equatins, = ma = ma ne in the -directin and ne in the -directin. r bjects at rest, the acceleratin is zer. B ewtn s secnd law, = ma, since the acceleratin is zer, the rce is zer. llwing is an eample prblem using ewtn s Secnd Law. Eample Prblem: Yu are helping a riend mve int a new apartnt. A b weighing 450kg needs t be mved t make rm r a cuch. Yu are taller than the b, s u dwn at an angle 50 degrees rm the hrizntal with a rce 1000 t tr t mve the b. The b des nt mve. (a) What is the rictinal rce while u are ing? Shw ur wrk. (b) Yur riend tries t mve the b with a rce 1100 at an angle 35 degrees. Yur riend cannt mve the b either. What is the rictinal rce while ur riend is ing? Shw ur wrk. (c) The ceicient static rictin between the b and the lr is I u and ur riend tgether, each ing with the sa rce and at the sa angle as u ed in parts a and b, can u mve the b? Eplain ur reasning. Part (a): (1) cus n the Prblem: What s ging n? 1

2 Yu n a b and it desn t mve. Yu want t ind the rictinal rce while u are ing n the b. Since the b is nt mving, the acceleratin is zer and the rce n the b is zer. Yu can use the act that the rce is zer in bth the - and - directins t ind the rictinal rce. (2) Describe the Phsics: What is the phsics? Draw a rce diagram r the b. Chse the -ais t be parallel t the rictinal rce and the -ais t be parallel t the nrmal rce. Appl ewtn s secnd law in bth the - and - directins. Use the act that the acceleratin is zer in bth the - and - directins: = ma = ma = 0 = 0 ind the rces in the - and - directins and the rce in each directin: = csθ = + = = + + cs = + + = θ + We are lking r, which we can slve r with the equatin r the rce in the - directin. 2

3 (3) Plan the Slutin: Can we ind the slutin? Using the act that = 0, we can slve r : = cs θ + (4) Eecute the Plan: What is the answer? = cs θ + 0 = 1000 cs50 = (5) Evaluate the Answer: Can this be true? The units are crrect. The rictinal rce is negative, which ans it is in the ppsite directin t the ing rce, which makes sense. Part (b): (1) cus n the Prblem: What s ging n? Yur riend es n a b and it desn t mve. Yu want t ind the rictinal rce while he is ing n the b. Since the b is nt mving, the acceleratin is zer and the rce n the b is zer. Yu can use the act that the rce is zer in bth the - and - directins t ind the rictinal rce. (2) Describe the Phsics: What is the phsics? Draw a rce diagram r the b. 3

4 Chse the -ais t be parallel t the rictinal rce and the -ais t be parallel t the nrmal rce. Appl ewtn s secnd law in bth the - and - directins. Use the act that the acceleratin is zer in bth the - and - directins: = ma = ma = 0 = 0 ind the rces in the - and - directins and the rce in each directin: = csθ = + = = + + = θ + cs sin + + = θ We are lking r, which we can slve r with the equatin r the rce in the - directin. (3) Plan the Slutin: Can we ind the slutin? Using the act that = 0, we can slve r : = cs θ + (4) Eecute the Plan: What is the answer? = cs θ + 0 = 1100 cs35 = (5) Evaluate the Answer: Can this be true? The units are crrect. The rictinal rce is negative, which ans it is in the ppsite directin t the ing rce, which makes sense. Part (c): 4

5 (1) cus n the Prblem: What s ging n? Yur riend and u are ing n a b. Yu want t knw i the b will mve. Yu need t ind the rce that u appl in the -directin and the maimum rictinal rce. Yu need t determine i the rce u are appling in the -directin is greater than the maimum rictinal rce, in which case the b wuld mve. (2) Describe the Phsics: What is the phsics? Draw a rce diagram r the b. Chse the -ais t be parallel t the rictinal rce and the -ais t be parallel t the nrmal rce. Appl ewtn s secnd law in bth the - and - directins. We can use the act that the acceleratin is zer in the -directin: = ma t ind the nrmal rce and the act that the maimum rictinal rce is related t the nrmal rce = µ ma s t ind the maimum rictinal rce. ind the ttal rce the in the -directin = = + riend riend csθ + csθ 5

6 Cmpare it t the maimum rictinal rce. I the ttal rce the is greater than the maimum rictinal rce then the b will mve. (3) Plan the Slutin: Can we ind the slutin? ind the rces in the -directin, slve r the nrmal rce and then slve r the maimum rictinal rce: riend = = = mg riend 0 = = = = + + riend riend riend riend Use the equatin belw t ind the maimum rictinal rce. = µ ma s ind the ttal rce the in the -directin = = + riend riend csθ + csθ Cmpare it t the maimum rictinal rce. (4) Eecute the Plan: What is the answer? Chse up as psitive, s rces pinting upward will be psitive and rces pinting dwnward will be negative. riend = 1000 sin 50 = 1100 sin 35 = 450kg(9.8m / s 2 ) = sin θ riend 6

7 = ( 1000)sin 50 = 5239 ( 1100)sin 35 2 ( 450kg(9.8m / s )) The maimum rictinal rce is ma ma ma = µ s = 0.45(5239) = 2358 ind the ttal rce the in the -directin = = = 1000 cs50 = riend csθ + riend csθ cs35 The rictinal rce is t the let and the rce the is t the right. The ttal rce the is less than the maimum rictinal rce, s the b will nt mve. (5) Evaluate the Answer: Can this be true? It makes sense that the b wuld nt mve. 7

PROBLEM 1-10 points. [ ] n 1 >n 2 >n 3 [ ] n 1 >n 3 >n 2 [ ] n 2 >n 1 >n 3 [ X ] n 2 >n 3 >n 1 [ ] n 3 >n 1 >n 2 [ ] n 3 >n 2 >n 1

PROBLEM 1-10 points. [ ] n 1 >n 2 >n 3 [ ] n 1 >n 3 >n 2 [ ] n 2 >n 1 >n 3 [ X ] n 2 >n 3 >n 1 [ ] n 3 >n 1 >n 2 [ ] n 3 >n 2 >n 1 PROBLEM - 0 pints [5 pints] (a) Three media are placed n tp f ne anther. A ray f light starting in medium experiences ttal internal reflectin at the tp interface but sme f the light refracts int medium