Answer to Question #125870 in Mechanics | Relativity for Sammy W-S

Question #125870
physics dynamics:
you are trying to hold your 550 g physics books with your hand against a vertical wall applying a 10 N force. Below the book on the floor you placed a motion sensor, the position time graph for the book decelerates at about a 45° angle. What is the coefficient of kinetic friction?
Expert's answer

Explanations & Calculations

  • The position-time (=distance-time) graph (considered for a instantaneous position in the motion) implies something that is shown in the figure above which says the book is experiencing a uniform velocity (Vu) due to the applied force instead of falling under gravity.
  • "\\small V_u = \\tan \\theta = \\tan(\\pi -45) = -1 \\implies V_u =\\downarrow 1ms^{-1}"

  • Forces in a system are in equilibrium along a direction with uniform velocity ("\\small \\because a = 0" ).
  • Therefore, considering the vertical equilibrium,

"\\qquad\\qquad\n\\begin{aligned}\n\\small \\mu R &= \\small 0.55g\\\\\n\\small \\mu_k &= \\small \\frac{0.55kg\\times9.8ms^{-2}}{10N}\\\\\n&= \\small \\bold{0.539}\n\\end{aligned}" "\\small R = 10N"

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