Answer:
The acceleration of an object hanging from a string can be determined using the formula:
a = (m_system * g - T) / (m_disk + m_system)
where:
a = acceleration
m_system = mass of the system (400 grams)
m_disk = mass of the disk (40 grams)
g = acceleration due to gravity (approximately 9.8 m/s^2 or 9.8 N/kg on the surface of the Earth)
T = tension in the string
Since T = m_disk * a, we can substitute that in and solve for a:
a = (m_system * g - m_disk * a) / (m_disk + m_system)
a * (m_disk + m_system) = m_system * g - m_disk * a
a * (m_disk + m_system) + m_disk * a = m_system * g
a * m_system + m_disk * a = m_system * g
a = m_system * g / (m_system + m_disk)
Plugging in the values:
a = 400g / (400 + 40)
a = 400g / 440
a = 9.09 g (approx)
So the acceleration is approximately 9.09 times the acceleration due to gravity.