Question

the position vector of the objects of masses 25kg and 10kg are (4,5,7)m and (1,3,5)m respectively . obtain the vector representating the gravitational force on 25kg object by 10kg object.

Answer 1

m1 = 4.0 kg         m2 = 2.0 kg

Given   vector  r1 =  3 t i + t  j + 2 t² k   m

            vector r2 = 3 i + (t² -1) j + 4 t k   meters

Position vector of Center of mass = r = (m1 r1  + m2 r2 )/ (m1+m2)

 r = [ (4* 3t + 2*3) i + (4* t+ 2* (t²-1)) j + (4*2t² + 2 * 4 t) k ]/(4+2)  meters

 = [ (12t +6) i + (2t² + 4t -2) j + (8t² + 8 t) k ] /6  m

Velocity of cm = v = dr/dt = 2 i + (2t+2)/3 j + (8 t + 4)/3 k    m

   magnitude = √(36+4t²+4+8t+64t²+16+16t)  /3  m

                     = √(17 t²+ 6t + 10) * 2/3  m

Acceleration of cm = a = dv/dt = 2/3 j + 8/3 k

    

Net force acting on the system =  (m1+m2) * a

         = 4 j + 16 k

   Magnitude = 4√17 Newtons