You have been hired to design a spring-launched roller coaster thatwill carry two passengers per car. the car goes up a 10-m highhill, then descends 15m to the track's lowest point. you'vedetermined that the spring can be compressed a maximum o 2.0m andthat a loaded car will have a maximum mass of 400kg. for safetyreasons, the spring constant should be 10% larger than the minimumneeded for the car to just make it over the top. a) what spring constant (k) should you specify ? b) what is the maximum speed of a 350 kg car if the spring iscompressed the full amount.

a) 21.6 KN/m

b)v = 18.56 m/s

Explanation:

For this problem, the spring should be strong enough to get the car just over the top so:

mgh = (1/2)kx^2

(400)*(9.8)*(10) = (0.5)*(k)*(2.0^2)

k = 39200/2.645

k = 19600 N/m

a) K increased by Increase by 10%, so:

k = 19600 * 1.10 = 21560 N/m = 21.6KN/m>specified spring constant

b) Now, Maximum speed of a 350 kg car will be at the bottom of the roller coaster:

therefore, (1/2)mv^2 + mg(Y_1-Y_2) = (1/2)kx^2

(0.5)*(350)*(v^2) + (350)(9.8)(10-15) =(0.5)*(21560)*(2.0^2)

v^2 = 344.4

v = 18.56 m/s

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm