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  4. In a truck-loading station at a post office, a small 0.200 kg package is released from rest at point A on a track that is one quarter of a circle with radius 1.5 m (figure). The size of the package is much less than 1.5 m, so the package can be treated as a particle. It slides down the track and reaches point B with a speed of 5 m / s. From point B, it slides on a level surface a distance of 2.5 m to point C, where it comes to rest. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/b2b084f5e35967c5ef693be142476931-.png /> What is the coefficient of kinetic friction on the horizontal surface?

Q. In a truck-loading station at a post office, a small $0.200\, kg$ package is released from rest at point $A$ on a track that is one quarter of a circle with radius $1.5\, m$ (figure). The size of the package is much less than $1.5\, m$, so the package can be treated as a particle. It slides down the track and reaches point $B$ with a speed of $5\, m / s$. From point $B$, it slides on a level surface a distance of $2.5\, m$ to point $C$, where it comes to rest.
image
What is the coefficient of kinetic friction on the horizontal surface?

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Solution:

The magnitude of the work done by friction is the kinetic energy of the package at point $B$,
or $\mu_{k} m g L=\frac{1}{2} m v_{B}^{2}$,
or $\mu_{k}=\frac{(1 / 2) v_{B}^{2}}{g L}$
$=\frac{(1 / 2)(5 m / s )^{2}}{\left(10 m / s ^{2}\right)(2.5 m )}=0.50$

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