First slide

Connected bodies

Question

A block of mass 3 kg which is on a smooth inclined plane making an angle of 30^o to the horizontal is connected by a cord passing over a light frictionless pulley to a second block of mass 2 kg hanging vertically. What is the acceleration of each block and what is the tension of the cord?

Moderate

A

0.98 m/s²; 17.6 N
B

1.98 m/s²; 19.6 N
C

0.49 m/s²; 9.8 N
D

1.47 m/s²; 4.9 N

Solution

$a = \left[ {\frac{{{m_2} - {m_1}\sin \theta }}{{{m_1} + {m_2}}}} \right]g = \frac{{2 - 3\sin {{30}^0}}}{5} \times 9.8$
$= \frac{{2 - 3/2}}{5} \times 9.8$
$= \frac{1}{{10}} \times 9.8 = 0.98\,\,m/{s^2}$
$\therefore T = \frac{{{m_1}{m_2}g(1 + \sin \theta )}}{{{m_1} + {m_2}}}$
$= \frac{{2 \times 3 \times 9.8\left( {1 + \frac{1}{2}} \right)}}{5} = 17.6N$

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