A system consists of two particles. At `t=0`, one particle is at the origin, the other, which has a mass of `0.60kg`, is on the y-axis at `y=80m`. At `t=0`, the centre of mass of the system is on the y-axis at `y=24m` and has a velocity given by `(6.0m//s)t^2hatj`.
(a) Find the total mass of the system.
(b) Find the acceleration of the centre of mass at any time t.
(c) Find the net external force acting on the system at `t=3.0s`.

Answer

A, B, C

Explanation

(a) `y_(CM)=(m_1y_1+m_2y_2)/(m_1+m_2)`
`:. 24=((0.6)(80)+(m_2)(0))/("Total mass")`
`:. "Total mass" =2kg`
(b) `a_(CM)=(d)/(dt)(v_(CM))=(d)/(dt)[6t^2]hatj`
`=(12t)hatjm//s^2`
(c) `F_(ext)=m_(CM) a_(CM)=m_(CM)(d)/(dt)(v_(CM))`
`=m_(CM)(12t)hatj`
At `t=3s`, `F_(ext)=(2kg)(12)(3)hatjN`
`=(72hatj)N`