(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of


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1 Homewok VI Ch. 7  Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the atio of the cicumfeence of the eath to its otational peiod. Thus, we find: v 2π T Thus, the centipetal acceleation is 2π(6373 km) 24h(3600 s ) km s 463 m s. h a v2 (463 m s ) km m s. 2 (b) Assuming the otational axis uns though the noth pole, the centipetal acceleation is simply a 0 m. s 2 Poblem 19 (a) The foce is simply given by F m v2 m (55.0 kg)(4.00 s ) N m (b) The skate s weight is simply mg 539 N. Thus, α F W m v2 mg v2 g Thus, the foce exeted on the skate is 2.04 times he weight. Poblem 22 The maximum lateal acceleation is simply 1
2 a max v2, (86.5 km h ) m, 1.23e8 m h 2, 9.46 m s 2, 0.97g. Poblem 25 (a) The tension is easily found fom T W b 0, T m b g, 9.8 N. (b) The hoizontal foce acting on the puck is simply the tension in the sting, namely, 9.8 N. (c) The speed of the puck can be found by fom the foce equation. So, T m tv 2, mb v g, m t 6.3 m s. Poblem 35 (a) The satellite s obital speed can be found fom the foce equation. That is, GMm 2 m v2, GM v 2, km. 2
3 Now, ecall that when using Newton s law of gavitation, the foce equation measues the adius fom the cente of the Eath. Thus, to find the altitude above the suface of the Eath, we must subtact off the adius of the Eath, leaving us with an altitude of 9570 km above the suface of the Eath. (b) The peiod of the satellite s obit is simply given by T 2π v, 2π( m) 5000 m, s s, 5.56 h. Poblem 43 (a) The tangential speed of the ball is simply (b) The centipetal acceleation is v 2πω 2.51 m s. a (2πω) m s 2. (c) Recall the above foce equation T mv2. Then, the maximum tangential speed that can be attained without beaking the ope is T v m 4.0m s. Poblem 51 See fee body diagam below. Fom the diagam, we see that the nomal foce is given by F N mω 2 75m. 3
4 Then, the vetical foce equation eads f  W 0. Thus, the minimum coefficient of fiction is µ W F N mg 75m g List the fou fundamental foces of natue. Compae thei basic popeties (ange, stength,...) in quantitative fashion. How do we see these foces demonstated in natue? 1. Gavity is weakest of the fou fundamental foces. All objects in the univese ae acted upon by the gavitational inteaction. The gavitational inteaction is esponsible fo apples falling to the eath and planets obiting the sun. Although it is so weak, gavity dominates on lage scales. It is esponsible fo the dynamics of galaxies and the lage scale stuctue and evolution of the univese. It has an infinite ange, and thus a massless caie paticle, the gaviton. In the limit of small masses, the foce is descibed well by Newton s law of gavitation. This states that the gavitational inteaction is of the fom F g GMm, whee G 6.67e11 N m2 is the gavitational 2 kg 2 constant. Fo an accuate desciption of gavity involving lage masses, one must go to Einstein s theoy of Geneal Relativity which is govened by the Einstein equations, G µν + Λg µν 8πT µν, whee G µν is the Einstein tenso and is given by G µν R µν 1 2 g µνr, whee R µν is the Ricci tenso, g µν is the metic tenso, and R is the scala cuvatue. T µν is the stessenegy tenso and Λ is the cosmological constant. Fo the puposes of this discussion, let s set the stength of gavity to The electomagnetic inteaction was the fist fo which a complete theoy was fomulated. It is actually the unification of two obseved inteactions, the electic and magentic. The electic foce is esponsible fo the attaction and epulsion of chages. In paticula, like chages epel while opposite chages attact. The magnetic foce is due to moving chage. Much expeimental wok in this aea was pefomed by Michael Faaday while theoetical unification was completed by James Clek Maxwell in The electic foce is of the fom F e kqq C 2 N m 2, whee k 1 2 4πɛ 0, whee ɛ e12 is the pemittivity of fee space. Togethe with the magnetic foce, the 4
5 Loenz foce equation takes the fom F q(e + v x B), whee E and B ae the electic and magnetic fields espectively. A consequence of electomagnetic theoy is the existence of electomagnetic adiation, of which visible light and adio waves ae two such examples. The electic foce, like gavity, is an invesesquae law foce. Thus, it too has infinite ange and a massless caie paticle (the photon). The elative stenth of the electic foce to the gavitational foce between a poton and an electon is given by F e F g ke 2 Gm p m e, 2.3e39! The electic foce is 39 odes of magnitude stonge than the gavitational foce! 3. The weak inteaction is a nuclea foce esponsible fo cetain types of nuclea decay. Much of the pioneeing wok in the aea was caied out by Enico Femi, amongst othes. The elative stength of the weak foce is appoximately 1 F 137 e, making it 37 odes of magnitude stonge than gavity. It tuns out that the electomagnetic and weak inteactions ae elated. Such a unification was accomplished by Sheldon Glashow, Steven Weinbeg, and Abdus Salaam, fo which they wee awaded the 1979 Nobel Pize in physics. The weak foce is of vey shot ange, appoximately m, giving it the shotest ange of any of the fou fundamental foces. Coesponding to such a shot ange, the weak foce has vey massive caie paticles, the positively and negatively chaged W bosons and the neutal Z boson. The weak inteaction is tied in with paticles known as neutinos, fo which Fed Reines, a pofesso at UC Ivine, eceived the 1995 Nobel Pize in physics fo his wok on these paticles. 4. The final fundamental foce is the stong foce. As suggested by its name, it is the stongest of the fundamental foces. It is a vey shot ange foce, acting ove the dimensions of the nucleus, appoximately m, and is esponsible fo holding the nucleus togethe, thus ovecoming the electic epulsion of the potons. The stong foce takes the fom F e, 2 whee m. Relative to the gavitational foce, the stong foce is ove 45 odes of magnitude stonge! 0 5
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