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4 years ago

11

Consider the two-body situation at the right. A 3.50x103-kg crate (m1) rests on an inclined plane and is connected by a cable to

a 1.00x103-kg mass (m2). This second mass (m2) is suspended over a pulley. The incline angle is 30.0° and the surface has a coefficient of friction of 0.210. Determine the acceleration of the system and the tension in the cable.

1 answer:

4vir4ik [10]4 years ago

4 0

Answer: $a=2.42 m/s^2$

Explanation:

Given

mass $m_1=3.50\times 10^{3} kg$

$m_2=1.00\times 10^{3} kg$

$\theta$ (inclination)= $30^{\circ}$

$\mu =0.21$

Let T be the tension in the rope

From Diagram

$m_1g\sin \theta -T-f_r=m_1a$ -----------------1

where $f_r=friction\ force$

$f_r=\mu m_g\cos \theta$

For block $m_2$

$T=m_2a$ -----------2

From 1 & 2

$m_1g\sin \theta -m_2a-\mu m_1g\cos \theta =m_1a$

$m_1g(\sin \theta -\mu \cos \theta )=(m_1+m_2)a$

$\frac{9.8\times 3.5\times 10^3}{4.5\times 10^3}(0.5-\0.21\cos 30)=4.5a$

$a=2.42 m/s^2$

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In order to answer part b, we must draw a free body diagram of us sitting on a chair. (See attached picture.)

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