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

Question

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?

Answer 1

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 (V_u) 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,

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