Posted by **Alphonse** on Thursday, October 25, 2012 at 1:31pm.

In the configuration shown (10m incline for m1 and 8m vertical length for m2 with a spring under it, both masses are linked by a rope and a pulley at the top), the 52.0 N/m spring is unstretched, and the system is released from rest. The mass of the block on the incline is m1 = 24kg and the mass of the other block is m2 = 5kg. (Neglect the mass of the pulley.). If the coefficient of kinetic friction between m1 and the incline is 0.24, then how fast (in m/s) are the blocks moving when m1 has slid 0.90 m parallel to the incline (and the 5.00 kg block has gained 0.90 m in elevation)?

- Physics -
**Elena**, Thursday, October 25, 2012 at 2:54pm
Initial heights of the blocks: m1 -> H; m2 -> h

Initial energy of the “two blocks” system is

E1 = m1•g•H+m2•g•h

When the blocks covered s=0.9 m the energy of ”two blocks+spring” system is

E2= m1•g(H-s•sinα) +m1•v²/2 {m2•g(h+s) +m2•v²/2 +ks²/2.

From the law of conservation of energy

E1-E2 =W(fr)

W(fr) =μ•m1•g•cosα•s.

m1•g•H+m2•g•h- m1•g(H-s•sinα) - m1•v²/2 {m2•g(h+s) - m2•v²/2 -ks²/2 = μ•m1•g•cosα•s.

v=sqrt[{ 2gs(m1•sinα-m2)-kx²-2•μ•m1•g•cosα•s}/(m1+m2)]

I got v= 2.26 m/s. Check my calculations.

- Physics -
**AH**, Thursday, October 25, 2012 at 9:27pm
Sorry, how did you get the angle and what is x?

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