Question

Suppose an Atwood machine has a mass of m1 = 6.0 kg and another mass of m2 = 2.0 kg hanging on opposite sides of the pulley. Assume the pulley is massless and frictionless, and the cord is ideal. Determine the magnitude of the acceleration of the two objects and the tension in the cord.

Answer 1

Acceleration=
`4.9 /s^2`

Tension=29.4 N

Step-by-step explanation:

We are given that

`m_1=6 kg`

`m_2=2 kg`

We have to find the magnitude of the acceleration of the two objects and the tension in the cord.

Tension,
`T=m_1(a+g)`

`m_2g-T=m_2a`

Substitute the values

`m_2g-m_1(a+g)=m_2a`

`m_2g-m_1a-m_1g=m_2a`

`g(m_2-m_1)=m_2a+m_1a=a(m_1+m_2)`

`a=((m_2-m_1)g)/(m_1+m_2)`

Substitute the values

`a=((2-6)* 9.8)/(2+6)=-4.9m/s^2`

Where
`g=9.8m/s^2`

Hence, the magnitude of the acceleration of the two objects =
`4.9 m/s^2`

Substitute the values of a

`T=m_1(a+g)=6(-4.9+9.8)=29.4 N`