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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 6 / Problem 6.70

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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A net force along the x-axis that has x-component is

Chapter 6, Problem 6.70

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QUESTION:

A net force along the x-axis that has x-component \(F_x=-12.0\mathrm{\ N}+ \left(0.300 \mathrm {\ \ N}/ \mathrm{m}^2 \right)x^2\) is applied to a 5.00-kg object that is initially at the origin and moving in the -x-direction with a speed of 6.00 m/s. What is the speed of the object when it reaches the point x = 5.00 m?

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QUESTION:

A net force along the x-axis that has x-component \(F_x=-12.0\mathrm{\ N}+ \left(0.300 \mathrm {\ \ N}/ \mathrm{m}^2 \right)x^2\) is applied to a 5.00-kg object that is initially at the origin and moving in the -x-direction with a speed of 6.00 m/s. What is the speed of the object when it reaches the point x = 5.00 m?

ANSWER:

Step 1 of 2

Provided, $F(x)\ =\ -12.0\ N\ +\ (0.300\ N/{m}^{2}){x}^{2}$

Initial speed of the object, $u\ =\ 6.00\ m/s$

Distance it moved, $x\ =\ 5.00\ m$

Force required to move from origin to $x\ =\ 5.00\ m$

$F\ =-12.0\ N\ +\ (0.300\ N/{m}^{2})\ {5}^{2}\ {m}^{2}/{s}^{2}$

$F\ =-\ 12.0\ N\ +\ 7.5\ N\ =-4.5\ N$

Work done to move $5\ m$ is, $W\ =\ Fx\$

$W\ =-4.5\ N\times{}5\ m\ =-22.5\ J$

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