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ASHA 777 [7]
3 years ago
8

A force in the + x-direction with magnitude F(x) = 18.0N -(0.530 N/m)x is applied to a 6.00-kg box that is sitting on the horizo

ntal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box. If the box is initially at rest at x=0, use the work-energy theorem to determine its speed after it has travelled 14.0 m?
Physics
1 answer:
gogolik [260]3 years ago
5 0

Answer:v=8.17 m/s

Explanation:

Given

F(x)=18-0.530 x

mass of box=6 kg

distance traveled is 14 m

Work done by force

W=\int_{0}^{14}Fdx

W=\int_{0}^{14}(18-0.53x)dx

W=\left ( 18x-\frac{0.530}{2}x^2\right )_0^{14}

W=252-51.94=200.06 J

Work done by the force is equal to change in kinetic energy

W=\frac{mv^2}{2}

200.06\frac{6\times v^2}{2}

v=8.17 m/s

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