A $221g$ block is moving on a frictionless surface at angle $=32$ as shown in Figure $1.$ It

hits a spring of spring constant $k=1\mathrm{.}2\frac{N}{c}m$ and the block compresses the spring $10\mathrm{.}5cm$

before coming momentarily to rest. Over the distance the spring is compressed, how much

work is done by

a$)$ the force of gravity and

b$)$ the spring?

c$)$ What was the speed of the block just before it hit the spring?

d$)$ If the surface is not frictionless, but instead has a coefficient of friction of ${}_k=\mathrm{.}12,$ find

the new answer to c$).$