You arc designing a new roller-coaster. The main feature of this particular desi
ID: 1483497 • Letter: Y
Question
You arc designing a new roller-coaster. The main feature of this particular design is to be a vertical circular loop-the-loop where riders will feel like they are being squished into their seats even when they are in fact upside-down (at the top of the loop). The coaster, mass 1000 kg, starts at rest a height of 80 m above the ground, speeds up as it descends to ground level, and then enters the loop which has a radius of 20 m. Suppose a rider is sitting on a bathroom scale that initially reads 980 N =W (when the coaster is horizontal and at rest). What will the scale read when the coaster is moving past the top of the loop? (You can assume the (he coaster rolls on (he track without friction) what is the final velocity, Vf at the top of theloop?Explanation / Answer
a)
By Conservation of energy
KEi+PEi =KEf+PEf
(1/2)mVi2+mgYinitial = (1/2)mVf2+mg(2R)
gYinitial=(1/2)Vf2+2gR
Vf2 =2[gYinitial-2gR] =2[9.8*80-2*9.8*20
Vf=28 m/s
Centripetal force
Fc=mVf2/R =1000*282/20
FC=39200 N
At the top of the loop net force is given by
Fnet=W+FN
So Normal Force
FN=FNet-W =39200-9800
FN=29400 N
b)
final velocity at the top of the loop is
Vf=28 m/s
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