If a $4 k g$ $4 kg$ object moving at $6 \frac{m}{s}$ $6 m/s$ slows to a halt after moving $35 m$ $35 m$ , what is the coefficient of kinetic friction of the surface that the object was moving over?

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If a $4 k g$ $4 kg$ object moving at $6 \frac{m}{s}$ $6 m/s$ slows to a halt after moving $35 m$ $35 m$ , what is the coefficient of kinetic friction of the surface that the object was moving over?

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Answer 1 · 2016-02-27T05:08:23

$μ_{k} = 0.0525$ $\mu_k=0.0525$

Explanation:

Since the object is moving on a plane surface, the kinetic friction experienced by the object will be $μ_{k} m g$ $\mu_kmg$ implying that the de-acceleration due to friction will be $μ_{k} g$ $\mu_kg$

So, using the third kinematic equation
$v^{2} = v_{o}^{2} + 2 a x$ $v^2=v_o^2+2ax$

The object is said to have come to a halt so that means $v = 0 m s^{- 1}$ $v=0ms^-1$
So, $v_{o}^{2} = 2 a x$ $v_o^2=2ax$ (we ignored the negative sign since we know why that's there).

So, we know it travels a distance of $35 m$ $35m$ before it stops so $x = 35 m$ $x=35m$ . We know it initially had a speed of $6 m s^{- 1}$ $6ms^-1$ so $v_{o} = 6 m s^{- 1}$ $v_o=6ms^-1$ .

So, $a = \frac{v_{o}^{2}}{2 x} = \frac{6^{2}}{2 \cdot 35} = \frac{36}{70} = 0.51$ $a=v_o^2/(2x)=6^2/(2*35)=36/70=0.51$
So, $a = 0.51$ $a=0.51$ . But $a = μ_{k} g$ $a=\mu_kg$ So, $0.51 = μ_{k} \cdot 9.8 \Rightarrow μ_{k} = \frac{0.51}{9.8}$ $0.51=\mu_k*9.8\implies\mu_k=0.51/9.8$

Solving it yourself, you now understand that things look odd even if they are right.

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If a $4 k g$ $4 kg$ object moving at $6 \frac{m}{s}$ $6 m/s$ slows to a halt after moving $35 m$ $35 m$ , what is the coefficient of kinetic friction of the surface that the object was moving over?

1 Answer

Explanation:

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If a 4kg4 kg object moving at 6ms6 m/s slows to a halt after moving 35m35 m, what is the coefficient of kinetic friction of the surface that the object was moving over?

1 Answer

Explanation:

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If a $4 k g$ $4 kg$ object moving at $6 \frac{m}{s}$ $6 m/s$ slows to a halt after moving $35 m$ $35 m$ , what is the coefficient of kinetic friction of the surface that the object was moving over?