Consider a solid sphere of mass m and radius r being released down a ramp from...

Consider a solid sphere of mass m and radius r being released down a ramp from a height h (i.e., its center of mass is initially a height h above the ground). It rolls without slipping and passes through a vertical loop of radius R.

a. Determine the moment of inertia of the solid sphere. You must carry out the integration and it’s not sufficient just to write out 2/5mr^2

b. Use energy conservation to show that the tangential and angular velocities of the sphere when it reaches the top of the loop is v=sqrt[((10g)/7)*(h-2R+r)], ?=sqrt[((10g)/(7r^2))*(h-2R+r)]

c. Draw a force diagram for the sphere at the top of the loop and write down Newton ?s second law in the radial direction.

d. Show that the minimum height from which the sphere must be released so that it doesn’t fall off the track atthe top of the loop is 2.7R-1.7r.

e. Neglecting its moment of inertia, would the minimum height be more or less than the one you calculated? Explain

Expert Solution

3rd part answer is unclear. its N=mgcos(teta)

genius_generous answered 2 years ago

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