Question

the list of equations to list are attached! thanks!

6. A playground merry-go-round, i.e., a horizontal disc of radius 3 m that can rotate about a vertical axis through its center, is rotating at an angular speed 1/s (measured, as usual, in terms of radians). The moment of inertia of the merry-go-round with respect to that axis is 3000 kg m? A student of mass 80 kg is standing at the center of the merry-go-round. The student now walks outward all the way to the edge and stops there, holding tight onto a handle. Determine the angular speed once the student has arrived at the edge, and the work the student has performed. Submit your answer in the following form: • Referring to the numbered equation list attached to the end of the exam, list only the equation numbers relevant for this problem. • Give the numerical value of the moment of inertia of the system once the student has arrived at the edge . Give your numerical answer for the angular speed once the student has arrived at the edge. . Give your numerical answer for the work the student has performed. 7. A spacecraft of mass 4 . 10 kg is in a circular orbit of radius R = 5000 km around a planet. The speed of the spacecraft on the orbit is 50 km/s. Determine the mass of the planet and the energy of the spacecraft. Submit your answer in the following form: • Referring to the numbered equation list attached to the end of the exam, list only the equation numbers relevant for this problem. Give your numerical answer for the mass of the planet. • Give your numerical answer for the energy of the spacecraft. 8. An oscillator is carrying out simple harmonic motion in the 2-direction. Each time it passes through the equilibrium position, it has speed 2.0 m/s. The angular frequency of the oscillation is 4.0/s (given, as usual, in terms of radians). Determine the amplitude of the oscillation; furthermore, if the harmonic oscillator happens to be part of a medium sustaining a sinusoidal wave of wavelength = 0.40 m, determine the wave speed in the medium. Submit your answer in the following form: • Referring to the numbered equation list attached to the end of the exam, list only the equation numbers relevant for this problem. . Give your numerical answer for the amplitude of the oscillation. . Give your numerical answer for the wave speed in the medium.

Answer 1

Oprob => 633 phong growd merry-go-romedi 2 Imgr 3000 kg-ml, Radii =R= 3m initial speed W, = 1 sadlie student mass &m=song Cigo gy R R (23) ► momentofinestia 9 → Po Angularspoo -list of equation 16 can be used in las fine related to this prob. ment of inertion of the system ince the student has arrived at the edge & Iq = Ingot more? = 3000 (809) I2 37 20 kg-my Anguilar speed once stwork atledge Angular momentima conserved so that L = 72 = 22 22 12,w, - initial vahee W = LW, Lozi (student at centre) 3000 the edge: 3720 I262 - student at xi radise A2 = 0.806 rad see o work done by the stient Snergij conservation principle- b = Ef w r * WE & IN (1 + 2 12) *3000* 1*(1 +39 3720) = 27097 Joule

spacecraft mass = m = = 4x10²ng circular orbit-radirer= 5000km. Чред = Turfша) Left say: mass of the planet =M We canwrite, for stable equilibrium mor GMm R2 o mass of the planet smo no pa Box103)'xsnorros 6067x10-11 53x1011 667x10- 1.879x1026kg M 0 Energy of the spacecraft êmor GMM som GmM @ mura_9x10%(57109)" R 2R for 2 B to - 5x1012 Jorge equationen (26),(25), 29,6 -related to this pooblem. ® at equilibrium at tato An oscillator_intre xdirection at equilibrium - speed & 2.0 mysee W-40 raise Amplitude of the oscillation Ribe A costutto) attato) A = 2/2 1/2ml xfto) =0 = A cos@toros) Ato; to. 19 = 1/2 je (t) = . An sinato 19) 222 Aw.sin 7,200

3 m af & o Ware speed in the medium - Were length of the sinusoidel ware - 2 Yemen At 31 as 9.40m. 040 X 4.0 20.255 my see prelocin 2 08 0.255 afsee o list of the equations equi's (24), 32).(29) -- refuted to this poob.