On a frozen pond, a 10-kg sled is given a kick that imparts to it an initial speed of $v_0$ = 2.0 m/s

# On a frozen pond, a 10-kg sled is given a kick that imparts to it an initial speed of $v_0$ = 2.0 m/s

Asked by 3 years ago
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On a frozen pond, a 10-kg sled is given a kick that imparts to it an initial speed of $v_0$ = 2.0 m/s.  The coefficient of kinetic friction between sled and ice is $\mu_k$ = 0.10.  Use the work-energy theorem to find the distance the sled moves before coming to rest.

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JasonJones

Answered by 3 years ago
389.5k points

The work energy theorem states that the work done is equal to the change in kinetic energy:

$W= \Delta KE = KE_f - KE_i$

where the kinetic energy is:

$KE=\frac{1}{2} mv^2$

In this case, the work done by friction is equal to the change in kinetic energy (work energy theorem).

$W = \Delta KE \,\,\, \to \,\,\, \mu_k m g \Delta x = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2$

and since $v_f$ = 0,

$\mu_k m g \Delta x = - \frac{1}{2} m v_i^2 \,\,\,\to\,\,\, \Delta x=-\,\,\frac{v_i^2}{2\mu_k g}=-\,\,\frac{(2.0 \, m/s)^2}{2(0.10)(-9.8 \, m/s^2)}=1.02 \, m$

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