A car of mass m, traveling at constant speed, rides over the top of a circularly shaped hill as shown.

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1 A ca of mass m, taveling at constant speed, ides ove the top of a ciculaly shaped hill as shown. The magnitude of the nomal foce N of the oad on the ca is. A) Geate than the weight of the ca, N > mg. B) Equal to the weight, N = mg. C) Less than the weight, N < mg. L16 W 10/1/14 a*e lectue 1

2 A ca of mass m, taveling at constant speed, ides ove the top of a ciculaly shaped hill as shown. N Wite NII: F net mg +x 0 < F net = ma = mv2 = mg N N < mg L16 W 10/1/14 a*e lectue 2

3 Assignments cuved mean = 75 About the exam: Raw aveage = 72. Each scoe is cuved upwad by 3 points. Student scoes (inceased by 3 points) ae posted on D2L. I have exam booklets fo the ealy exam pick up afte class today. See the couse web site fo suggestions about impoving in the futue. Any questions about you gade should be sent to Pof. Munsat. L16 W 10/1/14 a*e lectue 3

4 Assignments About the exam: Raw aveage = 72. Each scoe is cuved upwad by 3 points. Student scoes (inceased by 3 points) ae posted on D2L. I have exam booklets fo the ealy exam pick up afte class today. See the couse web site fo suggestions about impoving in the futue. Any questions about you gade should be sent to Pof. Munsat. Fo this week: Read Ch. 5 of Wolfson and Pof. Dubson s notes. Begin Ch. 6. Witten HW5, fom Red Wokbook. Scans of the Red and Blue Wokbooks ae on D2L. Fo next week: CAPA 6. Witten homewok 6: begin to analyze the Megawoosh video. L16 W 10/1/14 a*e lectue 4

5 Wi5en HW s 6-8: Megawoosh vs. Wateslide Wipeout Megawoosh Video: You Question fo HW6: Is tajectoy of this stunt theoetically consistent with Newton s Laws, if ai esistance and sliding fiction ae neglected? (Ignoe the ability of the man to suvive the landing in the kiddie pool.) Mythbustes Response: Myth Busted: Mythbustes conside accuacy and distance in the eal wold, whee sliding fiction and ai esistance exist. They find the accuacy is possible but distance is not unde ealistic conditions. L16 W 10/1/14 a*e lectue 5

6 Dynamics: Newton s Laws of Motion Applications: (1) Sliding Blocks. (2) Contact Foces. (3) Suspended Bodies. (4) Cicula Motion. (5) Fiction. L16 W 10/1/14 a*e lectue 6

Atwood machine Mass suspended fom anothe

a M m T a +x a = M 2 M 1 + M 2 g M 2 +x F g

7 Atwood machine Mass suspended fom anothe suppoted mass T a = M m M + m g M 1 +T +x T a M m T a +x a = M 2 M 1 + M 2 g M 2 +x F g =Mg F g =mg F g = M 2 g +x 1) Choose a coodinate system. 2) Specify the foces (fee-body diagam). 3) Conside F net = ma fo each object. 4) Solve fo what s needed. 5) Does the esult make sense? L16 W 10/1/14 a*e lectue 7

8 Dynamics: Newton s Laws of Motion Applications: (1) Sliding Blocks. (2) Contact Foces. (3) Suspended Bodies. (4) Cicula Motion. (5) Fiction. L16 W 10/1/14 a*e lectue 8

9 Example 2. A mey-go-ound has a adius = 5 m. If it s pushed to have a peiod of τ = 3 sec. = 5 m a R = 22 m/s 2 τ = 3 sec m = 25 kg a R = v2 = 4π 2 τ 2 What s the centipetal foce needed to hold a m = 25 kg gil on the mey-go-ound? F = m a R = 25 kg (22 m/s 2 ) = 550 N (1 lb/4.45 N) = 123 lb L16 W 10/1/14 a*e lectue 9

10 Example 3. The Eath cicles the Sun at an aveage distance of 1 AU = 1.5 x m in 1 yea. What is its obital centipetal acceleation? = 1 AU E a R = v2 = 4π 2 τ 2 = 4π 2 (1.5x10 11 m) (πx10 7 s) 2 1g = 6x10 3 m/s 2 9.8m/s % of g L16 W 10/1/14 a*e lectue 10

Example 3. The Eath cicles the Sun at an aveage distance of 1 AU = 1.5 x 10 11 m in 1 yea. What is its obital centipetal acceleation? = 1 AU τ = 365 days E a R = v2 = 4π 2 τ 2 0.

11 Example 3. The Eath cicles the Sun at an aveage distance of 1 AU = 1.5 x m in 1 yea. What is its obital centipetal acceleation? = 1 AU τ = 365 days E a R = v2 = 4π 2 τ % of g What s causing the centipetal acceleation? A) The electostatic foce between the Eath and Sun. B) The tension in the sting connecting the Eath to the Sun. C) The foce of gavity between the Eath and the Sun. D) Depends on the time of day. L16 W 10/1/14 a*e lectue 11

Example 3. The Eath cicles the Sun at an aveage distance of 1 AU = 1.5 x 10 11 m in 1 yea. What is its obital centipetal acceleation? = 1 AU E a R = v2 = 4π 2 τ 2 0.

12 Example 3. The Eath cicles the Sun at an aveage distance of 1 AU = 1.5 x m in 1 yea. What is its obital centipetal acceleation? = 1 AU E a R = v2 = 4π 2 τ % of g a R τ = 365 days It points towads the Sun at all times, which may be in the sky o not depending on the time of day. You e on the Eath. Which diection does the centipetal acceleation point? A) Down B) Up C) Depends on the time of yea. D) Depends on the time of day. L16 W 10/1/14 a*e lectue 12

13 Conside the following two situations: Situation I: A ca on Eath ides ove the top of a ound hill, with adius of cuvatue = 100 m, at constant speed v = 35 mph. Situation II: A monoail ca in integalactic space (no gavity) moves along a ound monoail, with adius of cuvatue = 100 m, at constant speed v = 35 mph. Which ca expeiences the lage acceleation? A) Eath ca. B) Space ca. C) Both have the same acceleation. Both cas have the same acceleation. The pesence of gavity doesn t change the fact that the acceleation has magnitude a = v 2 /. L16 W 10/1/14 a*e lectue 13

14 A ball of mass m is twiled on a sting in a vetical cicle of adius in the pesence of gavity with a constant speed v. At which position is the magnitude of the net foce on the ball geatest? (Ignoe ai esistance but conside gavity.) v F net Top T 1 = mv2 Bottom L16 W 10/1/14 a*e lectue 14 T 2 v A) Top B) Bottom C) Somewhee between Top and Bottom. D) Same at all positions.

15 A ball of mass m is twiled on a sting in a vetical cicle of adius in the pesence of gavity with a constant speed v. What is the elation between the magnitude of the tension in the sting at the top and bottom of the cicle? (Ignoe ai esistance but conside gavity.) v Top T 1 A) T 1 = T 2 B) T 1 > T 2 Bottom T 2 v C) T 2 > T 1 D) Impossible to tell fom the infomation given. L16 W 10/1/14 a*e lectue 15

16 A ball of mass m is twiled on a sting in a vetical cicle of adius in the pesence of gavity with a constant speed v. What is the elation between the magnitude of the tension in the sting at the top and bottom of the cicle? (Ignoe ai esistance but conside gavity.) v Top Top Bottom T 1 T 2 +x a +x T 1 m mg m mg a Bottom T 2 T 2 > T 1 v F net = ma = m v2 = T 1 + mg T 1 = mv2 mg F net = ma = m v2 = T 2 mg T 2 = mv2 + mg L16 W 10/1/14 a*e lectue 16

Chapter 5: Uniform Circular Motion

Chapter 5: Uniform Circular Motion Chapte 5: Unifom Cicula Motion Motion at constant speed in a cicle Centipetal acceleation Banked cuves Obital motion Weightlessness, atificial gavity Vetical cicula motion Centipetal Foce Acceleation towad