You\'re in an orbiting spacecraft at an altitude where the force of gravity is j

Question

You're in an orbiting spacecraft at an altitude where the force of gravity is just 42% of what it is on the earth's surface. Meanwhile, here on the surface of the earth, three friends are bored (and envious) as you orbit. At the playground. they start pushing on a frictionless merry-go-round (carousel), which has a moment of inertia about its center of I. The initial forces and directions are shown here (as viewed from above), and they continue pushing so that each torque remains. as it was initially. All this pushing begins at the moment when your orbiting spacecraft is directly overhead, and all pushing ceases after a time interval Delta t. Measuring from the start of their pushing, how many revolutions has the merry-go-round made by the lime your spacecraft passes directly overhead again (i.e. on its next revolution)? (You may assume that the time interval Deltat end, before you complele your next revolution. ) You may consider these values as known: g earth, r earth, I, F1, l1, theta1, F2, l2, theta2, F3, l3,theta3, Delta t.

Explanation / Answer

Angular acc of spaceship = ^2*R

and Force = GMm/R^2 = m*.42g => R = Rearth(Radius of earth)/.42

=> = .42*(g/Rearth)

Now Consider Merry go round

Net external moment = F1*l1*sin(1) + F2*l2*sin(2) + F3*l3*sin(3) = I*' ,get '

Now time taken by spaceship for 2/(.42*(g/Rearth)) = t1

in that time t1 angle revolved = t1*'

therefore no of revolutions = 2/(t1*')

=>Finally no of revolutions = 2/(t1*(F1*l1*sin(1) + F2*l2*sin(2) + F3*l3*sin(3))/I)

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.