A rollercoaster car may be represented by a block of mass 50. 0kg . The car is r

Question

A rollercoaster car may be represented by a block of mass 50. 0kg . The car is released from rest at a height h = 60. 0m above the ground and slides along a frictionless track. The car encounters a loop of radius R = 20. 0m at ground level, as shown. As you will learn in the course of this problem, the initial height 60. 0m is great enough so that the car never loses contact with the track. Find an expression for the kinetic energy K of the car at the top of the loop. Find the minimum initial height h min at which the car can be released that still allows the car to stay in contact with the track at the top of the loop.

Explanation / Answer

kinetic energy at the top of the loop = mgh =   mg (60-40) = 50* 10* 20 = 1000 j

centripital force due to mg = mv^2/r

v^2 =gr or v = sqrt ( 200) = 14 .1421 m/s

so at least the velocity at the top most point should be this much

to keep that min. velocity at the point it shud have the corrosponding kinetic energy

: 0.5 m * 200 = m g* h

h = 10 so the initial position shud at least be 10 m above the highest point in the loop

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