= v 2. a c. = G m m 1 2. F g G = Review 5: Gravitation and Two-Dimensional Motion

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1 Review 5: Gavitation and Two-Dimensional Motion Review 5 Gavitation and Two-Dimensional Motion 2 d = 1 2 at F = ma 1. A busy waitess slides a plate of apple pie alon a counte to a huny custome sittin nea the end of the counte. The custome is not payin attention, and the plate slides off the counte hoizontally at 0.84 m/s. The counte is 1.38 m hih. a. How lon does it take the plate to fall to the floo? b. How fa fom the base of the counte does the plate hit the floo? 2. The Moon evolves aound Eath in a cicula obit with a adius of m. It takes 27.3 days fo the Moon to complete one obit aound Eath. What is the centipetal acceleation of the Moon? 3. A clown ides a small ca at a speed of 15 km/h alon a cicula path with a adius of 3.5 m. a. What is the manitude of the centipetal foce on a 0.18 k ball held by the clown? b. At the point whee the ca is headed due noth, the clown thows the ball vetically upwad with a speed of 5 m/s elative to the movin ca. To whee must a second clown un to catch the ball the same distance above the ound as it was thown? 4. A 0.45 k ball is attached to the end of a cod of lenth 1.4 m. The ball is whiled in a cicula path in a hoizontal plane. The cod can withstand a maximum tension of 57.0 N befoe it beaks. What is the maximum speed the ball can have without the cod beakin? net a c = v 2 = G m m 1 2 G = N m 2 k 2 5. A mable olls off the ede of a table that is m hih. The mable is movin at a speed of m/s at the moment that it leaves the ede of the table. How fa fom the table does the mable land? 6. A ca movin at m/s ounds a bend in the oad. The bend is semicicula and has a adius of 60 m. What is the centipetal acceleation of the ca? 7. A town has a lae clock on the hall in the town squae. The clock has hands that show the hous, minutes, and seconds. A fly is sittin on the tip of the hand that shows the seconds. If the lenth of the hand is 1.2 m, what is the fly s centipetal acceleation? 8. A ock is tied to a stin and spun in a hoizontal cicle. The stin is 1.8 m lon and the ock has an acceleation of 3.4 m/s 2. What is the tanential velocity of the ock? 9. The mass of Eath is k, the mass of the Moon is k, and the mean distance of the Moon fom the cente of Eath is km. Use these data to calculate the manitude of the avitational foce exeted by Eath on the Moon. 10. Two identical bowlin balls ae placed 1.00 m apat. The avitational foce between the bowlin balls is N. Find the mass of a bowlin ball.

2 Review 5: Gavitation and Two-Dimensional Motion 11. A plane dops a escue capsule fom an altitude of 8500 m. a. How lon does it take fo the capsule to fall to Eath, assumin ai esistance is neliible? b. If the plane is tavelin with a hoizontal speed of 483 km/h when the capsule is eleased, what is the hoizontal distance between the point at which the capsule is eleased and the point at which the capsule stikes the ound? 12. A satellite is placed in a cicula obit 100 km above Eath s suface. Eath s mass is k and its aveae adius is m. a. What is the speed of the satellite? b. How many minutes does it take the satellite to complete one obit? 13. The asteoid Vesta has a mass of k and an aveae adius of 510 km. a. What is the acceleation due to avity at its suface? b. How much would a 95 k astonaut weih at the suface of Vesta? 14. The mass of Eath is k and the mass of the Sun is 330,000 times eate than the mass of Eath. If the cente of Eath is, on aveae, m fom the cente of the Sun, calculate the manitude of the avitational foce the Sun exets on Eath. 15. Two metal sphees, each weihin 24 k ae placed 0.05 m apat. Calculate the manitude of the avitational foce the two sphees exet on each othe. 16. A ca and a tuck ae tavelin side by side on the hihway. The ca has a mass of k and the tuck has a mass of k. If the cas ae sepaated by 2.1 m, find the foce of avitational attaction between the ca and the tuck. 17. A 5 k mass weihs 8.1 N on the suface of the Moon. If the adius of the Moon is 1737 km, what is the mass of the Moon? 19. Acceleation due to avity on Eath s suface is 9.80 m/s 2. Thus, a 1.00 k mass weihs 9.80 N on the suface of Eath. If the adius of Eath was cut exactly in half but the mass of Eath emained unchaned, how much would a 1.00 k mass weih on the suface of Eath?

3 Review 5: Gavitation and Two-Dimensional Motion 1a s 1b. Δd = v 2( 1.38 m) ( 0.53 s) Δd = 0.84 m/s Δd = 0.45 m days = s Δd 2π 2π m s 1022 m/s m/s m m/s 2 3a. 15 km/h = 4.17 m/s F = mv2 ( 0.18 k) 4.17 m/s F = 3.5 m F = 0.89 N 2 3b. It will take 1 s fo the ball to etun so it will o 4.17 m F = mv2 F m ( 57 N) 1.4 m 0.45 k 13.3 m/s 0.39 s Δd = v 2( m) ( 0.39 s) Δd = m/s Δd = m m/s 60 m 2.7 m/s 2 Δd 2π 60 s 2π 1.2 m m/s m/s 1.2 m m/s 2

4 Review 5: Gavitation and Two-Dimensional Motion a. a 1.8 m 3.4 m/s m/s m 1 m 2 2 F= N m 2 /k 2 ( k) ( k) ( m) 2 F = N 2 m = F2 G m = ( N) 1.00 m G m = 6.8 k 41.6 s 2( 8500 m) 11b. 483 km/h = 134 m/s Δd = v Δd = 134 m/s 2 ( 41.6 m/s) Δd = 5588 m 12a. F c = F G 12b. 13a. mv 2 = GMm 2 GM G( k) m m 7840 m/s Δd Δd v 2π v 2π m m 7840 m/s 5190 s 86 min = GM 2 = G k m 2 = m/s 2 13b. = m 14. = ( 95 k) m/s 2 = 7.3 N m 1 m 2 2 ( k) ( ) ( k) ( m) 2 F= N m 2 /k 2 F = N

5 Review 5: Gavitation and Two-Dimensional Motion ( 24 k) 24 k 0.05 m F = N 2 2 ( 1370 k) 9920 k 2.1 m F = N 2 M = F2 Gm m 2 M = 8.1 N G 5 k M = k 18. If the adius was half, the foce would incease by a facto of 4, thus a 1.00 k mass would weih 39.2 N

Extra notes for circular motion: Circular motion : v keeps changing, maybe both speed and

Extra notes for circular motion: Circular motion : v keeps changing, maybe both speed and Exta notes fo cicula motion: Cicula motion : v keeps changing, maybe both speed and diection ae changing. At least v diection is changing. Hence a 0. Acceleation NEEDED to stay on cicula obit: a cp v /,