Calculating Velocity: Roofer's Toolbox Sliding on a 36deg Slanted Roof

[rezal]

Hello, I'm practicing by doing the problems in my textbook but I have no way of knowing if my answers to positive questions are correct or not so can someone tell me if I did this problem correctly?

1. Homework Statement
While a roofer is working on a roof that slants at 36deg above the horizontal, he accidentally nudges his 85.0-N toolbox, causing it to start sliding downward, starting from rest. If it starts 4.25 m from the lower edge of the roof, how fast will the toolbox be moving just as it reaches the edge of the roof if the kinetic friction force on it is 22.0 N?

Homework Equations

KE + U + W = KE + U sin(theta)=o/4.25

The Attempt at a Solution

U + W = KE o=4.25sin36=2.49
mgcos(theta)(h)+wsin(theta)(u_k)=KE
(85*cos(36)*2.49)+(85*sin(36)*22)=KE
KE=1270.38
v=sqrt((2*KE)/m)
V=17.12 m/s?

 

[Simon Bridge]

Welcome to PF;
If you don't know if the answer is correct or not, then you did not understand the work. You are, after all, training to be able to solve problems where nobody knows the answers so the sooner you start figuring out how to gain confidence in your own work the better.

The way to gain confidence is to write out your reasoning, and reality check the results. Here you write out, in words, what the energy transformations are.
Then write down an energy equation that says the same thing.
Then go through the factors in the energy equation and write them out in terms that you are given ...

It is also best practice to sub numbers in at the very end if at all possible - do the algebra first.

Off the first glance, you should take another look at the energy calculations ... 22N is the friction force, so you don't need the coefficient of kinetic friction to calculate it. You are given the weight, so you don't need mg in your equation. the distance to the edge reads to me like the distance along the roof ... stuff like that.