Asked by JasonJones 3 years ago

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 lancer 3 years ago

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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Asked: 3 years ago