Three uniform spheres are fixed at the positions shown in Fig. P13.43. If the sp

Question

Three uniform spheres are fixed at the positions shown in Fig. P13.43.

If the spheres are in deep outer space and a 0.0150kg particle is released from rest 300m from the origin along a line 45 degree below the negative x-axis, what will the particle's speed be when it reaches the origin?

Three uniform spheres are fixed at the positions shown in Fig. P13.43. If the spheres are in deep outer space and a 0.0150kg particle is released from rest 300m from the origin along a line 45 degree below the negative x-axis, what will the particle's speed be when it reaches the origin?

Explanation / Answer

Kinetic Energy of particle=-PE at origin+PE at the other position PE at 300m=-Gm1m2/r Since the distance is very large we can assume that all 3 spheres are located at equal distance from the particle. PE=G*0.15*(1+2+1)/300 =-0.002G PE at origin =-(1/0.5 +1/0.5 + 2/0.5*2^0.5)*G*0.015 =-0.102G Applying the formula o.5*m*v^2=0.1G v=2.98*10^-5 ms^-1

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