Question $1$

As shown in the figure, a massless spring with spring constant $k=200\frac{N}{m}$ is attached to a pole and the

free end of the spring is compressed by $50$ centimeters by pushing a block of mass $0\mathrm{.}25kg$ against it$.$ The

spring$-$block was then released with zero initial velocity. When the spring regains it's natural length, the

block leaves the spring and starts moving along the horizontal plane in the rightward direction. The block

then passes through a path with friction $(x=0$ meter to $x=5$ meters$)$ and then starts moving along an

inclined plane. All other portion except that $5$ meters is frictionless.

$($a$)$ If the zero of gravitational potential energy is at a height of $2$ meters below the horizontal plane

where the spring$-$block system is$,$ and the zero of spring potential energy is at it's equilibrium position,

calculate the total potential energy of the spring$-$block system when it was compressed by $50cm.$

$($b$)$ Calculate the work done by the friction force when the block moves from $x=0$ to $x=5($in meters$).$

$($c$)$ Calculate the speed of the block when it reaches the topmost edge of the inclined plane.

$($d$)$ Calculate the time that the block will take to reach the horizontal plane after it's launch from the topmost edge of the inclined plane.