Winter 2008 Midterm (modified to be a chapter 8, energy-type question) A 15 kg b

Question

Winter 2008 Midterm (modified to be a chapter 8, energy-type question) A 15 kg block is on a 10 m long and 8 m high incline. It is attached via a light rope that passes over a light, pulley on a frictionless axis to a 5 kg block which is attached to the top of a spring with a spring constant of 24 N/m that is initially neither stretched nor compressed. When released from rest, the 15 kg block starts sliding down the incline. (Use g=10 m/s2.) Find the common speed of the two blocks when the 15 kg block has slid 0.5 m down the incline assuming the incline is frictionless. Repeat part a) assuming the coefficient of kinetic friction between the incline and the 15 kg block is muk=0.20.

Explanation / Answer

a)

conservation of energy:

Ei = Ef

Ei = 0 >>>> Ef = 0

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Ef = (1/2) k x2 + m1 g x - m2 g (x sin) + 0.5 (m1+m2) v2

0 = 0.5*24*(0.5*0.5) + 5*10*0.5 - 15*10*(0.5*(8/10)) + 0.5*(5+15) v2

0 = -32 + 10 v2

>>> v = 1.79 m/s

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b)

fk = N = mg cos

Ef + fk x = (1/2) k x2 + m1 g x - m2 g (x sin) + fk x + 0.5 (m1+m2) v2

0 = (1/2) k x2 + m1 g x - m2 g (x sin) - ( m2 g cos) x + 0.5 (m1+m2) v2

0 = 0.5*24*(0.5*0.5) + 5*10*0.5 - 15*10*(0.5*(8/10)) + 0.20*15*10*(6/10) + 0.5*(5+15) v2

0 = -14 + 10 v2

>>>> v = 1.18 m/s

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