( ) Tutorial 1 Practice, page (a) Given: d = 324 m or r = 162 m; F c = F g Required: v. Analysis: F c. = mv2 ; F g = mg. F c.

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Download "( ) Tutorial 1 Practice, page (a) Given: d = 324 m or r = 162 m; F c = F g Required: v. Analysis: F c. = mv2 ; F g = mg. F c."

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1 Section 3.4: Rotatin Fames of Refeence Mini Investiation: Foucault Pendulum, pae 128 Answes may vay. Sample answes: A. The otation does not affect the pendulum mass. Fom ou fame of efeence, the mass swins back and foth consistently while the lobe otates beneath it. B. Fom ou fame of efeence, the peiod of otation does not affect the mass. To an obseve on the lobe, the faste the otation of Eath, the faste the pendulum appeas to move. This implies that the otation of Eath causes the movement of the Foucault pendulum. C. At the equato the pendulum would not shift at all. Tutoial 1 Pactice, pae a) Given: d 324 m o 162 m; F c F Requied: v mv2 ; F m F c F mv 2 m v 2 v Solution: v 9.8 m/s ) m) v 39.8 m/s Statement: The elative speed of the astonauts is 39.8 m/s. b) Given: ; 162 m Requied: T Analysis: 4! 2 T 4! 2 Solution: T 4! 2 4! m 9.8 m s 2 & T 26 s Statement: The peiod of the otation of the spacecaft is 26 s. Copyiht 2012 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3.4-1

2 2. Yes, both would expeience atificial avity equal to about 30.0 of Eath s avity, o The mass cancels out in the equation to detemine speed, so the effect is independent of mass. 3. Given: m/s 2 ; a net 9.70 m/s 2 ; m Requied: T Analysis: 4! 2 ; the centipetal acceleation is the diffeence between the acceleation due to avity and the net acceleation expeienced by a fallin object. 4! 2 a net 4! 2 4! 2 T a net Solution: T 4! 2 a net 4! m ) m s 9.70 m & 2 s 2 ) s 1 min 1 h 60 s 60 min T 7.9 h Statement: The lenth of the day, o peiod of the planet, is 7.9 h. 4. Given: m 1 56 k; 250 m; m 2 42 k Requied: v mv2 ; F m; the acceleation on the space station is o 3 4 because the scale eads the astonaut s weiht as 42 k instead of 56 k. F c F N mv m v that of Eath v 3 4 Copyiht 2012 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3.4-2

Solution: v 3 4 162 m 3 9.8 m/s2 4 v 43 m/s Statement: The space station floo otates at a speed of 43 m/s. 5. Given: 6.

3 Solution: v m m/s2 4 v 43 m/s Statement: The space station floo otates at a speed of 43 m/s. 5. Given: m Requied: v mv2 ; F m; the speed of the ca would make the centipetal foce eate than the avitational foce. F c F mv 2 m v 2 v Solution: v 9.8 m/s ) !10 6 m) v 7.9!10 3 m/s Statement: The ca would need a speed of m/s. Section 3.4 Questions, pae At just the iht speed, the centifual acceleation is enouh to povide enouh foce to keep the wate in the bucket. 2. The spinnin washin machine ceates entifual acceleation that foces wate in the clothes to the oute wall and thouh poes in the wall, thus emovin excess wate fom the clothes. 3. a) b) Copyiht 2012 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3.4-3

4 c) d) Given: 2.7 m; m 120 o 0.12 k; T 2.9 s Requied: θ Analysis: The hoizontal component of the tension F T balances the centipetal foce and the vetical component of the tension F T balances the avitational foce. Expess the tanent atio of the anle in tems of the applied foce and the avitational foce, then solve fo the anle; v 2! T tan! F c F 2 mv &! tan 1 m v 2 &! tan 1 Solution: Detemine the speed 2.7 m fom the cente: v 2! T 2! 2.7 m) 3.9 s) m/s two exta diits caied) v 4.3 m/s Detemine the anle the stin makes with the vetical: v 2 &! tan m 2 & & tan 1 s 2.7 m ) 9.8 m & s two exta diits caied)! 36 Statement: The stin makes a 36 anle with the vetical. e) Given: 2.7 m; m k; θ Requied: F T Analysis: The vetical component of the tension F T balances the avitational foce. Expess the cosine atio of the anle in tems of the tension and the avitational foce. Copyiht 2012 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3.4-4

5 cos! F F T F T F cos! F T m cos! Solution: F T m cos! 9.8 m s k F T 0.96 N & cos35.57 Statement: The tension in the stin is 0.96 N. 4. Given: m; T 24 h Requied: at the equato Analysis: Eath is a non-inetial fame of efeence. The acceleation of an object at the equato is the diffeence between the acceleation due to avity and the centifual acceleation,. Use 4! 2 to detemine the centifual acceleation, then calculate its atio with. Solution: Detemine the centipetal acceleation at the equato: 4! 2 24 h 4! m ) 60 min 1 h 60 s 1 min 4! m s) m/s 2 Theefoe, the atio of the centifual acceleation to is: & m/s2 9.8 m/s 2 ) Statement: The acceleation at the equato is 0.34 less that. 2 Copyiht 2012 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3.4-5

6 5. Given: d 10 m o 5 m; T 30 s; d 1.7 m Requied: compae at and d Analysis: 4! 2 Solution: Detemine the centipetal acceleation at the astonaut s feet: 4! 2 4! 2 5 m 30 s) m/s 2 Detemine the centipetal acceleation at the astonaut s head: 4! 2! d) 4! 2 5 m 1.7 m 30 s) m/s 2 Statement: The movie did not et the physics iht. The acceleation expeienced by the astonaut is in the ane of 0.05 m/s 2 to 0.07 m/s 2 instead of 9.8 m/s a) Given: 100 m; Requied: T Analysis: 4! 2 4! 2 T 4! 2 Solution: T 4! 2 4! m 9.8 m s 2 & s two exta diits caied) T s Statement: The peiod of otation is s. Copyiht 2012 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3.4-6

7 b) Given: 100 m; Requied: v Analysis: v2 v Solution: v! 9.8 m s 2 & 100 m) m/s two exta diits caied) v 31 m/s Statement: The speed of otation is 31 m/s. c) Given: 100 m; v i m/s; v 4.2 m/s Requied: F N mv ; F 2 N F c Solution: F N mv2 m m/s! 4.2 m/s) m) m 7.34 m/s 2 ) F N 7.3m Statement: The appaent weiht is 7.3 times the mass. d) Given: 100 m; v i m/s; v +4.2 m/s Requied: F N mv ; F 2 N F c Solution: F N mv2 m m/s m/s) m) m 12.6 m/s 2 ) F N 13m Statement: The appaent weiht is 13 times the mass. e) Runnin with the diection of the otation is a bette wokout because you expeience a eate centifual foce and it equies moe effot o exetion. 7. a) Given: m 65 k; 150 m; F N 540 N Requied: Analysis: F N F c ; F c m ; F N m Copyiht 2012 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3.4-7

8 Solution: F N m 540 N ) 65 k) m/s 2 two exta diits caied) 8.3 m/s 2 Statement: The acceleation of objects nea the floo of the space station is 8.3 m/s 2. b) Given: 150 m; m/s 2 Requied: v Analysis: v2 v Solution: v! m s 2 & 150 m) m/s two exta diits caied) v 35 m/s Statement: The speed of otation of the oute im is 35 m/s. c) Given: 150 m; m/s 2 Requied: T Analysis: 4! 2 4! 2 T 4! 2 Solution: T 4! 2 4! m m s 2 & T 27 s Statement: The peiod of otation of the space station is 27 s. 8. a) Given: 3.4 cm o m; f Hz Requied: Analysis: 4! 2 f 2 Copyiht 2012 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3.4-8

9 Solution: 4! 2 f Hz) 2 4! m m/s 2 Statement: Fom Eath s fame of efeence, the manitude of the centipetal acceleation is m/s 2. b) Answes may vay. Sample answe: Centifues need hih fequencies to et the eatest possible acceleation. A hih centifual foce moves the dense paticles to the bottom of a test tube, pefectly sepaatin mixed solutions such as plasma and ed blood cells. c) Answes may vay. Sample answe: By sepaatin paticles, medical eseaches can study the paticles in thei pue fom. 9. Answes may vay. Sample answe: A lae-scale centifue, like all centifues, spins to sepaate a mixtue into its components. In a lae-scale centifue, a wastewate mixtue is spun and wate is sepaated fom the heavie mixtue, often called slude, which settles on the bottom. The thickened mixtue is moved to anothe facility fo teatment while the wate is sent on fo diffeent teatment befoe etunin to the envionment. By sepaatin wate fom the heavie mixtue, these two components of wastewate can eceive the appopiate teatment befoe etunin to the envionment. Copyiht 2012 Nelson Education Ltd. Chapte 3: Unifom Cicula Motion 3.4-9

As observed from the frame of reference of the sidewalk:

As observed from the frame of reference of the sidewalk: Section 3.1: Inetial and Non-inetial Fames of Refeence Tutoial 1 Pactice, page 110 1. (a) When the ca is moving with constant velocity, I see the ball lie still on the floo. I would see the same situation