183_notes:examples:sliding_to_a_stop

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183_notes:examples:sliding_to_a_stop [2014/09/16 07:27] – pwirving183_notes:examples:sliding_to_a_stop [2014/09/22 04:18] – pwirving
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 === Facts ==== === Facts ====
 +
 +Block is metal.
 +
 +Mass of metal block = 3 kg
 +
 +The coefficient of friction between floor and block = 0.4
 +
 +Initial velocity of block = $\langle 6, 0, 0\rangle m/s$
  
 === Lacking === === Lacking ===
 +
 +Time it takes for the block to come to a stop.
 +
 +The distance the block moves during this time.
  
 === Approximations & Assumptions === === Approximations & Assumptions ===
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 === Representations === === Representations ===
  
-==== Solution ====+{{183_notes:friction_ground.jpg}} 
 + 
 +$\Delta \vec{p} = \vec{F}_{net} \Delta t$ 
 + 
 +=== 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} $ 
 + 
 +$ \Delta(t) = \dfrac{6 m/s}{0.4 (9.8 N/kg)} = 1.53s $ 
 + 
 +Since the net force was constant, $v_{x,avg} = (v_{xi} + v_{xf})/2$, so 
 + 
 +$ \Delta x/\Delta t = ((6 + 0)/2) m/s = 3m/s $ 
 + 
 +$ \Delta x = (3 m/s)(1.53 s) = 4.5m $
  • 183_notes/examples/sliding_to_a_stop.txt
  • Last modified: 2018/02/03 23:24
  • by hallstein