A block is released from rest, determine its velocity

[Alexanddros81]

Homework Statement

14.10 Solve Prob. 12.47 by the work-energy method

12.47 When the 1.8-kg block is in the position shown, the attached spring is
undeformed. If the block is released from rest in this position, determine its velocity
when it hits the floor

Homework Equations

The Attempt at a Solution

Here is my solution to both 12.47 and 14.10.
I get in 14.10 the correct answer but I am confused with 12.47. Is it correct?

 

[TSny]

When you wrote

you assumed $\int a dx = a \Delta x$. Is this true if the acceleration is not constant?

What is the main topic of chapter 12?

 

[Alexanddros81]

Hi! After reading a sample problem of the book I came up with the above solution.
I have a question though: If I integrate both sides of the equation just above equation (3)
shouldn't I be getting on both sides a constant C that cancels out?

 

[TSny]

View attachment 217021
I have a question though: If I integrate both sides of the equation just above equation (3)
shouldn't I be getting on both sides a constant C that cancels out?

Each side of the equation would have its own constant of integration. You can combine the two constants into one constant. Then, this constant is determined by the initial conditions as you have done.

Your work here is essentially the derivation of the work-energy principle for this particular problem.

 

[Alexanddros81]

Ok thanks for that.
I need to revise my calculus.

Alexandros