A $0\mathrm{.}50$ kg block rests on a frictionless level surface next to a spring. The spring$/$block system is compressed $7\mathrm{.}3$ cm and released. The spring returns to equilibrium and the block keeps moving at a speed of $3\mathrm{.}4$ m$/$s horizontally along a frictionless surface. After a short distance, it hits a $35$ cm long patch with a coefficient of kinetic friction of $0\mathrm{.}43.$ Beyond that stretch, the level surface becomes frictionless again. $7)$ What is the spring constant of the spring? a$)230$ N$/$m b$)140$ N$/$m c$)30$ N$/$m d$)1100$ N$/$m e$)730$ N$/$m $8)$ How much thermal energy is added to the floor and block as the block moves over the rough surface? a$)0\mathrm{.}11$ J b$)0\mathrm{.}74$ J c$)2\mathrm{.}2$ J d$)2\mathrm{.}9$ J e$)8\mathrm{.}6$ J $9)$ What is the speed of the block after passing over the $35$ cm rough stretch? a$)3\mathrm{.}3$ m$/$s b$)2\mathrm{.}9$ m$/$s c$)1\mathrm{.}7$ m$/$s d$)0\mathrm{.}8$ m$/$s e$)$ The block stops before the end of the rough stretch