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Physics Tutorial – Atwood’s Machine

Physics Tutorial Atwood Machine

Atwood’s machine is commonly used in the classroom to demonstrate the mechanical laws of motion with constant acceleration. This device consists of two masses connected by string over a frictionless pulley. This device is commonly used in a variety of grade 11 physics problems dealing with classical mechanics.

Example:

Two unequal masses are hung vertically over a frictionless pulley. If $m_1$ is 1.00 Kg and $m_2$ is 2.00 Kg, calculate the acceleration of the system and the tension in the string $($Gravity, $g = 9.81m/s^2)$.

Solution:

Since $m_1 > m_2$ the system will accelerate in favour of $m_2$ and therefore assigned a positive value. For mass 1 we find that:

$(1)$ $ \Sigma F_y = T – m_1g = m_1a$

For mass 2 we find that:

$(2)$ $ \Sigma F_y = T – m_1g = m_1a$

When equation (2) is subtracted from equation (1), the result is:

$(3)$ $ -m_1g + m_2g = m_1a + m_2a$

Substitute all known variables and solve:

$(4)$ $ (-1.00 x 9.81) + (2 x 9.81) = 1a + 2a$

$(5)$ $ 9.81 = 3a$

$(6)$ $ a = 3.27m/s^2$

Now that the acceleration of the system is known we can substitute the value of “a” into equation (1) to solve for T:

$(7)$ $ T – m_1g = m_1a$

$(8)$ $ T – 1.00(9.81) = 1.00(3.27)$

$(9)$ $ T – 9.81 = 3.27$

$(10)$ $ T = 13.08$ Newtons