Question

Evaluate the final kinetic energy of the supply spacecraft for the actual tractor beam force, F(x)=αx3+βF(x)=αx3+β.

α=6.1×10^−9 N/m^3
β=−4.1×10^6 N

Answer 1

1.1 x 10^10J

Step-by-step explanation:

∫x2,x1F(x)dx = ∫7.5 x 10^4 m ,0 (αx3+β)dx.

(αx4/4+βx) 7.5 x 10^4 m, 0

((6.1×10−9N/m3)( 7.5×104m)^4)/4 - (4.1×106N)( 7.5×104m) -0)

= 4.825 x 10^10 - 30.75 x 10^10

= 25.925 x 10^10J

= 2.5925 x 10^11J

The kinetic energy KE2 is,

KE2 = KE1 + ∫x2,x1F(x)dx

= 2.7×1011J - .5925 x 10^11J

= 0.1065 x 10^11J

= 1.1 x 10^10J