7. Back when I was a kid, I loved to play with my Hot Wheels. Hot Wheels are min

Question

7. Back when I was a kid, I loved to play with my Hot Wheels. Hot Wheels are miniature metal cars that race down lengths of flexible track. The track comes in segments that can be connected together. One thing you can do is make the cars Loop the Loop, as shown in the figure above. Starting at a height, h, the cars race down the track, traverse a circular loop of radius, R, without falling down at the top of the loop, and then continue racing along a section of level track. If the loop is 9 inches in diameter, what is the minimum height, h, from which the cars can start and still loop the loop without falling down at the top? Neglect friction and air resistance.

Explanation / Answer

given

d = 9 inch

= 9*2.54

= 22.86 m

= 0.2286 m

R = d/2

= 0.2286/2

= 0.1143 m

minimum speed at thr top of the loop, v = sqrt(g*R)

= sqrt(9.8*0.1143)

= 1.058 m/s

now apply conservation of energy

initial mechincal energy at height h = mehcnical energy at the top of the loop

m*g*h = m*g*(2*R) + (1/2)*m*v^2

h = 2*R + v^2/(2*g)

= 2*0.1143 + 1.058^2/(2*9.8)

= 0.286 m <<<<<<<<------------------Answer

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