Mechanics - 1

Classical Mechanics Level 3

Two blocks of mass $\text{5 kg}$ and $\text{3 kg}$ are suspended from a pulley with string $A$ . The pulley is hung from ceiling through another string $B$ . The tension in strings $A$ and $B$ are $T_A$ and $T_B$ newtons respectively. The blocks move with an acceleration $a \text{ m/s}^2$ .

Find the sum of the magnitudes of $a$ , $T_A$ , and $T_B$ .

Assumptions and Details:

Both strings are massless and inextensible.
The pulley is massless and frictionless between the strings and pulley.
Acceleration due to gravity $g = \text{10 m/s}^2$ .

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The answer is 115.

1 solution

Chew-Seong Cheong
Jan 25, 2019

By Newton's second law , the acceleration of the two blocks is given by:

$\begin{aligned} m_1 g - m_2 g & = (m_1+m_2) a \\ \implies a & = \frac {m_1-m_2}{m_1+m_2}g = \dfrac {5-3}{5+3}\times 10 = \text{2.5 m/s}^2 \end{aligned}$

The tension in string $A$ : $T_A = m_1g - m_1a = 5(10-2.5) = \text{37.5 N}$ .

The tension in string $B$ : $T_B = 2T_A = \text{75 N}$ .

Therefore, $|a|+|T_A|+|T_B| = 2.5+37.5+75 = \boxed{115}$ .

I just forget to multiply it by 2.

Origin X - 1 year, 11 months ago

Mechanics - 1

The answer is 115.

1 solution

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