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A box of unknown mass is sliding with an initial speed v = 4.80 m/s across a horizontal frictionless warehouse floor when it encounters a rough section of flooring d = 4.70 m long. Thecoefficient of kinetic friction between the rough section of flooring and the box is 0.100. Using energy considerations, determine the final speed of the box (in m/s) after sliding across the rough section of flooring.m/s

Answer :

Given data,

Initial speed of the box,

[tex]v=4.80\text{ m/s}[/tex]

Length of the floor,

[tex]d=4.70\text{ m}[/tex]

Coefficient of friction,

[tex]\mu_k=0.100[/tex]

Calculate the acceleration,

[tex]\begin{gathered} a=\text{coefficient of friction}\times g \\ a=0.100\times9.8 \\ a=0.98m/s^2 \end{gathered}[/tex]

Consider the kinematic equation of motion.

[tex]\begin{gathered} v^2=u^2-2ad \\ v^2=(4.80\text{ m/s})^2-2\times0.98m/s^2\times4.70\text{ m} \\ v^2=23.04-9.212^{} \\ v=3.717^{}\text{ m/s} \end{gathered}[/tex]

Therefore, the final speed of the box is

[tex]v=3.717\text{ m/s}[/tex]