Question 19 of 26 Map Sapling Learning macmillan learning You are designing the

Question

Question 19 of 26 Map Sapling Learning macmillan learning You are designing the section of a roller coaster ride shown in the figure. Previous sections of the ride give the train a speed of 16.1 m/s at the top of the incline, which is 37.9 m above the ground. As any good engineer would, you begin your design with safety in mind. Your local government's safety regulations state that the riders' centripetal acceleration should be no more than n1.57 g at the top of the hump and no more than N = 5.29 g at the bottom of the loop. For this initial phase of your design, you decide to ignore the effects of friction and air resistance What is the minimum radius you can use for the semi-circular hump? What is the minimum radius you can use for the vertical loop? Number Number In Im hump loop Tools x 10 37.9 m Rloop figure not to scale Previous Give Up &View; Solution Check Answer Next Exit Hint

Explanation / Answer

Apply conservation of energy

1/2 mv^2 + mgh = 1/2 m v'^2 + mg R hump

the relation between centripetal accleration and speed is

a= v'^2/Rhump

v'2 = aR hump

0.5 v^2 + gh = 0.5 ( aR hump)+ g R hump

0.5 ( 16.1)^2 + 9.8(37.9) = R hump ( 0.5 a + g)

R hump = 0.5 ( 16.1)^2 + 9.8(37.9)/( 0.5 ( 1.57 (9.8) + 9.8)

= 28.64 m

(b)

1/2 mv^2 + mgh = 1/2 m v'^2 =1/2 m ( a ' R loop)

R loop = v^2 + 2gh/ a'

= (16.1)^2 + 2 (9.8) (37.9)/5.29(9.8)

=19.32 m

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.