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Example: Sliding to a Stop
You take a 3 kg metal block and slide it along the floor, where the coefficient of friction is only 0.4. You release the block with an initial velocity of $\langle 6, 0, 0\rangle m/s$. How long will it take for the block to come to a stop? How far does the block move?
Facts
Lacking
Approximations & Assumptions
Representations
Solution
$ x: \Delta p_x = -F_N\Delta t $
$ y: \Delta p_y = (F_N - mg)\Delta t = 0 $
Combining these two equations and writing $ p_x = mv_x $, we have
$ \Delta(mv_x) = -mg\Delta t $
$ \Delta(v_x) = - g\Delta t $
$ \Delta(t) = \dfrac{\0 - v_{xi}}{-g} = \dfrac{\v_{xi}}{g} $