Determine a formula for the acceleration of each block

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Homework Statement


For two blocks, connected by a cord and sliding down the incline shown in the figure, describe the motion (a) if [tex]\mu_1 < \mu_2[/tex], and (b) if [tex]\mu_1 > \mu_2[/tex]. (c) Determine a formula for the acceleration of each block and the tension FT in teh cord in terms of m1, m2, and [tex]\theta[/tex]; interpret your results in light of your answers to (a) and (b).


Homework Equations


The Attempt at a Solution


http://img407.imageshack.us/img407/5930/chp5pro22nd5.th.png [Broken]
I need help on part c.

I got two equations in three unknowns ([tex]T, a_1, a_2[/tex]), and I don't know what to do:
[tex]m_1 g \sin \theta - F_{fk1} - T = m_1 a_1[/tex]
[tex]T + m_2 g \sin \theta - F_{fk2} = m_2 a_2[/tex]
[tex]F_{fk1} = \mu_1 N_1[/tex]
[tex]F_{fk2} = \mu_2 N_2[/tex]
 
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  • #2
PhanthomJay
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Homework Statement


For two blocks, connected by a cord and sliding down the incline shown in the figure, describe the motion (a) if [tex]\mu_1 < \mu_2[/tex], and (b) if [tex]\mu_1 > \mu_2[/tex]. (c) Determine a formula for the acceleration of each block and the tension FT in teh cord in terms of m1, m2, and [tex]\theta[/tex]; interpret your results in light of your answers to (a) and (b).


Homework Equations


The Attempt at a Solution


http://img407.imageshack.us/img407/5930/chp5pro22nd5.th.png [Broken]
I need help on part c.

I got two equations in three unknowns ([tex]T, a_1, a_2[/tex]), and I don't know what to do:
[tex]m_1 g \sin \theta - F_{fk1} - T = m_1 a_1[/tex]
[tex]T + m_2 g \sin \theta - F_{fk2} = m_2 a_2[/tex]
[tex]F_{fk1} = \mu_1 N_1[/tex]
[tex]F_{fk2} = \mu_2 N_2[/tex]
If the blocks move together with tension in the cord, their accelerations are equal. What if the tension in the cord is negative under this assumption?
 
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Oh I see...
So under the conditions of part (a), a1 = a2. And under the conditions of part (b), there is no tension. So now there's only two unknowns in two equations.
 
  • #4
PhanthomJay
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Oh I see...
So under the conditions of part (a), a1 = a2. And under the conditions of part (b), there is no tension. So now there's only two unknowns in two equations.
Yes, that is correct.
 

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