Math  /  Algebra

Question42. The device shown below is the Atwood's machine considered in Example 6.5. Assuming that the masses of the string and the frictionless pulley are negligible, (a) find an equation for the acceleration of the two blocks; (b) find an equation for the tension in the string; and (c) find both the acceleration and tension when block 1 has mass 2.00 kg and block 2 has mass 4.00 kg .

Studdy Solution
Substitute m1=2.00kg m_1 = 2.00 \, \text{kg} and m2=4.00kg m_2 = 4.00 \, \text{kg} into the equations for a a and T T .
Calculate acceleration a a :
a=(4.002.00)×9.812.00+4.00=2.00×9.816.00=3.27m/s2a = \frac{(4.00 - 2.00) \times 9.81}{2.00 + 4.00} = \frac{2.00 \times 9.81}{6.00} = 3.27 \, \text{m/s}^2
Calculate tension T T :
T=2×2.00×4.00×9.812.00+4.00=16.00×9.816.00=26.16NT = \frac{2 \times 2.00 \times 4.00 \times 9.81}{2.00 + 4.00} = \frac{16.00 \times 9.81}{6.00} = 26.16 \, \text{N}
The acceleration is 3.27m/s2 3.27 \, \text{m/s}^2 and the tension is 26.16N 26.16 \, \text{N} .

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