A small block of mass m starts from rest and slides along a frictionless loop-the-loop as shown in the sketch below. What should be the initial height z, so that m pushes against the top of the track (at a) with a force equal to its weight? Hints : When the small mass is at the top of the loop the net force is the centripetal force which is twice the gravitational force. mv² (i.e., = N + mg R where N is the normal force exerted by the loop pointing down). Mechanical Energy is conserved.

Physics for Scientists and Engineers, Technology Update (No access codes included)
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Chapter7: Energy Of A System
Section: Chapter Questions
Problem 7.5P: A block of mass m = 2.50 kg is pushed a distance d = 2.20 m along a frictionless, horizontal table...
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A small block of mass m starts from rest and slides along a frictionless loop-the-loop as shown in the sketch below.
What should be the initial height z, so that m pushes against the top of the track (at a) with a force equal to its
weight?
Hints : When the small mass is at the top of the loop the net force is the centripetal force which is
twice the gravitational force.
mv²
(i.e., N+ mg =
R
where N is the normal force exerted by the loop pointing down).
Mechanical Energy is conserved.
Transcribed Image Text:A small block of mass m starts from rest and slides along a frictionless loop-the-loop as shown in the sketch below. What should be the initial height z, so that m pushes against the top of the track (at a) with a force equal to its weight? Hints : When the small mass is at the top of the loop the net force is the centripetal force which is twice the gravitational force. mv² (i.e., N+ mg = R where N is the normal force exerted by the loop pointing down). Mechanical Energy is conserved.
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