Question

2.

If the system mass is 400 grams and the mass of the disks hanging on the string is 40 grams, predict the acceleration.

Answer 1

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.