Hi, can you please help me solve the following problem? It\'s notfrom a textbook

Question

Hi, can you please help me solve the following problem? It's notfrom a textbook, but we use the Giancoli Textbook as a resource.I can't figure this problem out. Please help me byproviding a step by step process of how you approached theproblem. Thank you!

Jupiter has the mass of 1.9 x 1027 kg. Its moonIo has the mass of 8.9 x 1022 kg, radius1,820km, and is orbiting Jupiter at the mean center-to-centerdistance of 422,000km. Consider an object on the surface ofIo at the point farthest from Jupiter.

a) By what percentage does the tidal force reduce itsweight? Ans: 0.51%.

b) If the surface of Io were covered by an oceanthat is 4.0km deep on average (in other words, about the sameaverage depth as on the Earth), estimate how large would the tidesbe, low-to-high? My teacher provided the followinganswer with hints: Let hlow and hhigh be the depths during low and high tides,respectively, and glow and ghighbe the effective accelerations due to gravity (with tidal forcesincluded) at the locations having these tides. Hydrostaticsdictates that the pressures at the bottom of the ocean should bethe same everywhere, or else the water would flow. Thus*glow*hlow = *ghigh*hhigh; thenhhighhlow works out to be about 20 m. However, Idon't know where to go with these hints. Please help, thankyou!

Explanation / Answer

the force acting between the Jupiter and its moonIo is F = (GMm/r2) ------------(1) the force between Jupiter and its moon Io isbalanced by the centripetal force acting on moon therefore weget F = (m * v2/r) -----------(2) from (1) and (2) we get (GMm/r2) = (m * v2/r) or v = (GM/r)1/2 ------------(3) G = 6.67 * 10-11 Nm2/kg2,M =1.9 * 1027 kg and r = 422,000 km = 422,000 *103 m substituting the above values in equation (3) we get the speedof moon around the Jupiter a)the tidal force acting on Jupiter is given by equation(1) the weight of Jupiter is given by w = Mg the percentage by which the tidal force reduce its weightis (F/w) * 100% b)According to Bernoulli's equation we have P1 + (1/2)v12 +glh1 = P2 +(1/2)v22 +ghh2 P1 = P2 and v1 =v2 or glh1 =ghh2 or (gl/gh) =(h2/h1) the height of the tides from low-to-high will be equal to theratio of the accelerations due to gravity gl andgh respectively.

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