# Determine a formula for the acceleration of each block

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

2. Homework Equations
3. 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 ($$T, a_1, a_2$$), and I don't know what to do:
$$m_1 g \sin \theta - F_{fk1} - T = m_1 a_1$$
$$T + m_2 g \sin \theta - F_{fk2} = m_2 a_2$$
$$F_{fk1} = \mu_1 N_1$$
$$F_{fk2} = \mu_2 N_2$$

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## Answers and Replies

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

2. Homework Equations
3. 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 ($$T, a_1, a_2$$), and I don't know what to do:
$$m_1 g \sin \theta - F_{fk1} - T = m_1 a_1$$
$$T + m_2 g \sin \theta - F_{fk2} = m_2 a_2$$
$$F_{fk1} = \mu_1 N_1$$
$$F_{fk2} = \mu_2 N_2$$
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?

Last edited by a moderator:
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.

PhanthomJay