Respuesta :
Answer:
K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x
Explanation:
To find the variation of kinetic energy, let's use the work energy theorem
W = ΔK
∫ F .dx = K -K₀
If the body starts from rest K₀ = 0
∫ F dx cos θ = K
Since the force and displacement are in the same direction, the angle is zero, so the cosine is 1
we substitute and integrate
α ∫ x³ dx + β ∫ dx = K
α x⁴ / 4 + β x / 1 = K
we evaluate from the lower limit F = 0 to the upper limit F
α (x⁴ / 4 -0) + β (x -0) = K
K = αX⁴ / 4 + β x
K = 1.525 10⁻⁹ x⁴ + 4.1 10⁶ x
in order to finish the calculation we must know the displacement
Answer:
1.1 x 10^10J
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
