In an Atwood machine

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

In an Atwood machine, two masses

m_1 = 2.0\,\text{kg}

and

m_2

(unknown) are connected by a light inextensible string passing over a smooth massless pulley. When the system is released, mass

m_1

is found to descend with a uniform acceleration of

0.30\,\text{m\,s}^{-2}

. (i) Derive an expression for the acceleration of the system in terms of

m_1

m_2

, and

g

. (ii) Hence obtain a formula for the unknown mass

m_2

in terms of

m_1

g

, and the measured acceleration

a

. (iii) Calculate the numerical value of

m_2

taking

g = 9.8\,\text{m\,s}^{-2}

. (iv) Briefly comment on whether

m_2

is greater than, less than, or equal to

m_1

, and relate this to the observed direction of motion.