A ball is placed against the inner edge of a cylinder at a height h =4R where R

Question

A ball is placed against the inner edge of a cylinder at a height h =4R where R is the radius of the cylinder. What initial horizontal speed v0 tangential to the cylinder wall should be given to the ball so that it will have completed exactly 2 revolutions around the inside of the cylinder when it hits the ground? Neglect friction and express your answer in terms of the variables given in the problem, (sec "Problem 1" figure below) While increasing speed, a train enters a 90 degree circular turn of radius R. At the point where it enters the turn, its speed is v0 and its acceleration in the direction tangent to its trajectory is half the magnitude of its centripetal acceleration. If the tangential acceleration remains constant throughout the turn, what is the centripetal acceleration just before the train leaves the curve? Express your answer in terms of the tangential acceleration, (sec "Problem 2" figure above)

Explanation / Answer

1)t=(2h/g)=2(2R/g)

v=R=(/t)R=4R/2(2R/g)

=*(2Rg)

2)R=v^2/2R

v_f=(v^2+2*(*R)*(R*/2))

accel=v_f^2/R

=(v^2/R)+R

=(v^2/R)(1+/2)

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