10kg sled is pushed with a initial speed of 2m/s. It has a coefficent of friction of .1. Using the work energy theorem how far does it travel before rest?

Question

10kg sled is pushed with a initial speed of 2m/s. It has a coefficent of friction of .1. Using the work energy theorem  how far does it travel before rest?

anonymous · Answer

The work energy theorem is stated as so:
$$W=\Delta KE$$or another way to represent it is this:$$Fd = \frac{ 1 }{ 2 }mv _{f}^{2}-\frac{ 1 }{ 2 }mv _{0}^{2}$$where "F" is the force by friction which is negative! since it's working against the initial velocity. You can use this formula to find the force due by friction:$$F _{\mu _{k}}=\mu _{k}N$$where N is your normal force which you can find out from the mass of the sled and the gravity constant.

Going back to your work energy theorem equation, we see that the final velocity is zero since it stops at that point, so your first term will clear out completely leaving you with your negative 2nd term. From there you can find "d" which represents how far the sled had slid with its initial velocity.