you are designing an amusement park ride. A cart with two riders moves horizonta

Question

you are designing an amusement park ride. A cart with two riders moves horizontally with speed v=6.00m/s. you assume that the total mass of the cart plus riders is 300kg. the cart hits a light   spring that is attached to a wall momentarily come to rest as the spring is compressed, and then regains the speed as it moves back in the opposite direction. for the ride to be thrilling but safe, the maximun acceleration   of the cart during this motion should be 3.00g. ignore friction, what is

a) the required force constant of the bring

b) the maximun distance the spring will be compressed.

Explanation / Answer

here,

horizontal speed , v = 6 m/s

mass of the cart , m = 300 kg

let the spring constant of the spring be k and compression in the spring be x

(a)

using conservation of energy

0.5 * m * v^2 = 0.5 * k * x^2

300 * 6^2 = k * x^2 ...(1)

and for the maximum accelration be a = 3 g

k*x/m = a

k*x = 300 * 3 * 9.8

k*x = 8820 ...(2)

from equation (1) and (2)

x = 1.22 m

k = 7229.51 N/m

a) the required force constant of the sring is 7229.51 N/m

b) the maximun distance the spring will be compressed 1.22 m

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