If an object is moving at $2 \frac{m}{s}$ $2 m/s$ over a surface with a kinetic friction coefficient of $u_{k} = \frac{17}{g}$ $u_k=17 /g$ , how far will the object continue to move?

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If an object is moving at $2 \frac{m}{s}$ $2 m/s$ over a surface with a kinetic friction coefficient of $u_{k} = \frac{17}{g}$ $u_k=17 /g$ , how far will the object continue to move?

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Answer 1 · 2016-05-07T08:02:20

$x = \frac{2}{17} = 0.11764$ $x=2/17=0.11764" "$ meter

Explanation:

Let $x$ $x$ be the distance

From $v_{f}^{2} = v_{0}^{2} + 2 a x$ $v_f^2=v_0^2+2ax$

$- F_{k} = m \cdot a$ $-F_k=m*a" "$ Kinetic Frictional force
$a = \frac{- F_{k}}{m}$ $a=(-F_k)/m" "$ acceleration

$F_{k} = μ_{k} \cdot F_{n}$ $F_k=mu_k*F_n" "$ Relation between Kinetic frictional force and the normal force

$F_{n} = m \cdot g$ $F_n=m*g$

$x = \frac{v_{f}^{2} - v_{0}^{2}}{2 a}$ $x=(v_f^2-v_0^2)/(2a)$

$x = \frac{v_{f}^{2} - v_{0}^{2}}{2 (\frac{- F_{k}}{m})}$ $x=(v_f^2-v_0^2)/(2((-F_k)/m))$

$x = \frac{v_{f}^{2} - v_{0}^{2}}{2 (\frac{- (μ_{k} \cdot F_{n})}{m})}$ $x=(v_f^2-v_0^2)/(2((-(mu_k*F_n))/m))$

$x = \frac{v_{f}^{2} - v_{0}^{2}}{2 (\frac{- (μ_{k} \cdot m \cdot g)}{m})}$ $x=(v_f^2-v_0^2)/(2((-(mu_k*m*g))/m))$

$x = \frac{v_{f}^{2} - v_{0}^{2}}{2 (- μ_{k} \cdot g)}$ $x=(v_f^2-v_0^2)/(2(-mu_k*g))$

$v_{f} = 0$ $v_f=0" "$ when it stops
$v_{0} = 2$ $v_0=2" "$ meter /second
$μ_{k} = \frac{17}{g}$ $mu_k=17/g$

$x = \frac{v_{f}^{2} - v_{0}^{2}}{2 (- μ_{k} \cdot g)}$ $x=(v_f^2-v_0^2)/(2(-mu_k*g))$
$x = \frac{0^{2} - 2^{2}}{2 (- (\frac{17}{g}) \cdot g)}$ $x=(0^2-2^2)/(2(-(17/g)*g))$

$x = \frac{- 4}{- 34} = \frac{2}{17}$ $x=(-4)/(-34)=2/17" "$ meters

God bless....I hope the explanation is useful.

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If an object is moving at $2 \frac{m}{s}$ $2 m/s$ over a surface with a kinetic friction coefficient of $u_{k} = \frac{17}{g}$ $u_k=17 /g$ , how far will the object continue to move?

1 Answer

Explanation:

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If an object is moving at $2 \frac{m}{s}$ $2 m/s$ over a surface with a kinetic friction coefficient of $u_{k} = \frac{17}{g}$ $u_k=17 /g$ , how far will the object continue to move?