use these $11$ protocols to solve the problem.

You should solve each of the following problems using the Conservation of Energy

protocol, showing all steps. Just to remind you, here are the protocol steps:

Step $1$: If there is not already a diagram provided, draw a diagram $($it does not need

to be a free$-$body diagram, just a diagram of the situation is best$).$

Step $2$: Identify, and put in writing, what the 'initial' and 'final' situations will be$.$

Step $3$: Make a list of all the forces that act on the object between the initial and

final situations

Step $4$: Classify each force as conservative or non$-$conservative

Step $5$: Calculate the work done by any non$-$conservative forces

Step $6$: Write down the Conservation of Energy theorem in symbols

Step $7$: On the left$-$hand side, substitute in the non$-$conservative works you found in

Step $5.$ On the right$-$hand side, substitute in all the relevant forms of energy,

as described in video.

Step $8$: If gravitational potential energy is among the energy relevant to the problem,

go back to the diagram and indicate where you are going to call $\text{'}$ h$=0\text{'}.$

Step $9$: Carefully think about the initial and final situation, and indicate whether any

of the energy terms on the right$-$hand side are zero in this problem. Don't

just erase them, but put in a 'goes to zero' arrow as in video.

Step $10$: Plug in the mathematical expression for each remaining form of energy:

K$=1//2$mv$^(2),$Ug$=$mgh$,$ and U$\_($sp$)=1//2$kx$^(2)$ using subscripts to indicate

initial or final, as appropriate.

Step $11$: Put in numbers and solve for the requested unknown.

A $1\mathrm{.}7$ kg block is attached to a spring of spring constant $140$N$//$m and the system is

'cocked' so that the spring is compressed by $18$ cm $.$ The block is released from rest

and moves up a rough $30^($@$)$ incline. If the coefficient of kinetic friction between the

block and the incline is $0\mathrm{.}3,$ what is the total distance traveled by the block from its

point of released to it high$-$end turnaround point?