Energy Problems (Help Greatly Needed)

[Double A]

I am having some difficulty answering a few problems on my physics homework.
I don't think that I am coming up with the right equations for given situations in the problems. The questions are as follows:

1. http://herograw.com/8-31.JPG

For this question I am getting - \frac{1}{2} m_1v^2 - \frac{1}{2} m_1v^2+m_2g\Delta h=-m_1\mu_kd where m₁ is the block in contact with the surface and m₂ is the hanging sphere. When I solve the equation for v (velocity), I get v=4.77 m/s. However, I should be getting a result of 3.74 m/s.

2. http://herograw.com/8-48.JPG

For this equation I get mgy_{max}-mgh=-mg \mu_k d but there needs to be something with the angle to derive that equation given in the problem.

3. http://herograw.com/8-60.JPG
http://herograw.com/figure8.60.JPG

When doing part (a) I was using the equation \frac{1}{2} m v^2+\frac{1}{2} k d^2=0to find d. I got d=0.424 m but for part (b) I would just get v=3 m/s which is given in the question when the object is moving to the right. I'm not sure if this is right or if I'm approaching the question correctly.

4. http://herograw.com/8-72.JPG

For this question I was able to find part (b) but I'm not sure how to start in finding part (a).

Any Help is greatly appreciated.

 

[Pyrrhus]

1)

You should have

\frac{1}{2}m_{1}v^2 + \frac{1}{2}m_{2}v^2 - m_{2}gh = -\mu m_{1}gh

2)
You should have

mgy_{max} - mgh = -\mu mgcos\theta \frac{y_{max}}{sin\theta}

3) Read the problem again you seem to forgot friction on this problem

 

[Double A]

I know that there is friction but when does it need to be accounted for?

If I were to use \frac{1}{2} mv^2+\frac{1}{2} kd^2=-\mu_kmgd I would have two variables to solve for because I do not know what the distance the block is sliding before it reaches the spring. Or are you saying that I need to use this equation for the other parts of the question if that is the right equation.