In outer space, far from other objects, block 1 of mass 30 kg is at position < 1

Question

In outer space, far from other objects, block 1 of mass 30 kg is at position < 11, 6, 0 > m, and block 2 of mass 800 kg is at position < 19, 6, 0 > m. At 4.2 seconds after noon both blocks were at rest at the positions given above. At 4.5 seconds after noon, what is the (vector) momentum of block 1?

Explanation / Answer

(a) In outer space, far from other objects, block 1 of mass 30 kg is at position < 11, 10, 0 > m, and block 2 of mass 1100 kg is at position < 17, 10, 0 > m. Mass = m1 =30 kg Location of m1 = vector r1=11i^+10j^ Mass = m2 =1100 kg Location of m2 = vector r2=17i^+10j^ Seperation between m2 and m1 =vector s = r1 - r2=- 6i^ Direction from m2 to m1 =unit vector =s^= - i^ Gravitation force (vector ) on block 2 due to block 1 =[Gm1m2/s^2]s^ Gravitation force (vector ) on block 2 due to block 1 =[6.67*10^-11*30*1100 / 6^2](-i^) (a) Gravitation force (vector ) on block 2 due to block 1 = [6.114*10^-8 N](-i) ______________________________________… Magnitude of Gravitational force on m1 =Magnitude of Gravitational force on m2 = F = 6.114*10^-8 N Acceleration of m2 =vector a2= F/m2= [6.114*10^-8 /1100 ](-i)=[5.558 *10^ -11 m/s^2](-i) time= t =4.4 - 4.1 =0.3 s (b) Momentum vector of block 2 =p2 =m2v2=m2a2t=[1.834*10^-8 kgm/s](-i) _____________________________________ Magnitude of Gravitational force on m1 =Magnitude of Gravitational force on m2 = F = 6.114*10^-8 N Acceleration of m1 = vector a1= F/m1=[ 6.114*10^-8 /30]i^ =[2.038 *10^ -9 m/s^2]i^ time = t =4.4 - 4.1 =0.3 s (c) Momentum vector of block 1 =p1 =m1v1=m1a1t=[1.834*10^-8 kgm/s](i)

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