You have been hired to design a spring-launched roller coaster that will carry two passengers per car. the car goes up a 12-m-high hill, then descends 18 m to the track's lowest point. you've determined that the spring can be compressed a maximum of 2.3 m and that a loaded car will have a maximum mass of 430 kg . for safety reasons, the spring constant should be 13 % larger than the minimum needed 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.

Vmax=11.53 m/s

Explanation:

from conservation of energy

     Spring potential energy =potential energy due to elevation

   0.5*k*x²= mg=mgh

   0.5*k*2.3²= 430*9.81*6

         k=9568.92 N/m

For safety reason

                                 k"=1.13 *k= 1.13*9568.92

                                    k"=10812.88 N/m

agsin from conservation of energy

    spring potential energy=change in kinetic energy

   0.5*k"*x²=0.5*m*

      10812.88 *2.3²=430*

           =11.53 m/s

atomic = no of protons.

mass number-atomic number = neutron number

convex lenses are thicker at the middle. rays of light that pass through the lens are brought closer together (they converge). a convex lens is a converging lens. when parallel rays of light pass through a convex lens the refracted rays converge at one point called the principal focus.