A force in the +x-direction with magnitude F(x)=18.0N?(0.530N/m)x is applied to

Question

A force in the +x-direction with magnitude F(x)=18.0N?(0.530N/m)x is applied to a 6.10 kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box.

Question 10 A force in the +z-direction with magnitude F(a) 318.0 N (0.530 N/m)z is applied to a 6.10 kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(z) is the only horizontal force on the box Part A If the box is initially at rest at z 0, what is its speed after it has traveled 16.0 m Express your answer to three significant figures and include the appropriate units v Value Units Submit My Answers Give Up

Explanation / Answer

let dx be the differential distance that the force moves the box.

The total work done on the box will be

U = Fdx from 0 to 16 meters

U = 18 - 0.530xdx from 0 to 16 meters

U = 18x - 0.265x² from 0 to 16 meters

U = 18(16) - 0.265(16²) - 0

U = 220.16 J

KE = U

½mv² = U

v = (2U/m)

v = (2(220.16) / 6.10)

v = 8.50 m/s

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