Mechanical energy of frictionless pulley

[Deadnotsleeping]

Homework Statement

In the system shown, the block M (mass of 15.65 kg) is initially moving to the left with a speed of 3.4 m/s The mass of m is 8.26 kg and the coefficients of friction are μs=0.411 and μk=0.304. The string is massless and the pulley is massless and frictionless. How fast will M be traveling when m has fallen through a height h=2.47 meters?

diagram: http://is.byu.edu/courses/univ/694820121008/media/8_problem_blockmass.jpg

Homework Equations

E_f - E_i = K_f - K_i + U_f - U_i = -fkd + ∑ W_otherforces

K = 1/2mv^2
U=mgy

The Attempt at a Solution

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Since M does not have any change in potential energy, but it is acted on by a tension force, I got

E_f - E_i = 1/2mv_f² - 1/2mv_i² = -fkd + T
where fkd = μ_kMgd and T = (( μ_k+1)Mg)/(1+M/m)

I solve for v_f but keep getting the wrong answer. The answer should be about 4.32 m/s
What am I doing wrong?

 

[BvU]

Hello DNS, welcome to PF !

I looks like you are adding an energy (f_kd) to a force (T) That can't be !

It also looks like your change in kinetic energy doesn't depend on M, which is very strange.

Finally, your energy balance should also have a term U_f - U_i which I miss in your solution attempt.

If you show your work, step by step, I may be able to answer your question. With the information you provide now it's impossible.

(And I do get 4.31 m/s if I use g = 9.81 m/s² )