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
365.9k points

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.

On a
JasonJones

1 Answer

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 $

Your Answer

Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0$ or $$\beta^2-1=0$$

Use LaTeX to type formulas and markdown to format text. See example.

Sign up or Log in

  • Answer the question above my logging into the following networks
Sign in
Sign in
Sign in

Post as a guest

  • Your email will not be shared or posted anywhere on our site
  •  

Stats
Views: 79
Asked: 3 years ago

Related