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geniusboy [140]
2 years ago
6

A particle of mass 4.0 kg is constrained to move along the x-axis under a single force F(x) = −cx3 , where c = 8.0 N/m3 . The pa

rticle’s speed at A, where xA = 1.0 m, is 6.0 m/s. What is its speed at B, where xB = −2.0 m?
Physics
1 answer:
Pie2 years ago
6 0

Answer:4.58 m/s

Explanation:

Given

mass of Particle m=4 kg

F=-cx^3

a=\frac{F}{m}

a=-\frac{cx^3}{m}

a=-\frac{8x^3}{4}

a=-2x^3

v\frac{\mathrm{d} v}{\mathrm{d} x}=-2x^3

vdv=-2x^3dx

integrating

\int_{6}^{v_b}vdv=\int_{1}^{-2}-2x^3dx

\frac{v_b^2-6^2}{2}=-\frac{1}{2}\left [ \left ( -2\right )^4-\left ( 1\right )^4\right ]

\frac{v_b^2-36}{2}=-0.5\times 15

v_b^2=36-15

v_b=\sqrt{21}

v_b=4.58 m/s

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