# If a 1 kg object moving at 1 m/s slows down to a halt after moving 1 m, what is the friction coefficient of the surface that the object was moving over?

May 19, 2017

The coefficient of friction is $= 0.051$

#### Explanation:

The coefficient of kinetic friction is ${\mu}_{k} = {F}_{r} / N$

The normal force is $N = 1 g N$

Initial velocity is $u = 1 m {s}^{-} 1$

Final velocity is $v = 0 m {s}^{-} 1$

Distance is $s = 1 m$

We apply the equation of motion

${v}^{2} = {u}^{2} + 2 a s$

$0 = 1 + 2 a$

$a = - \frac{1}{2} m {s}^{-} 2$

According to Newton's Second Law,

$F = m a$

${F}_{r} = 1 \cdot \frac{1}{2} = \frac{1}{2} N$

Therefore,

${\mu}_{k} = \frac{\frac{1}{2}}{1 g} = \frac{1}{2 g} = 0.051$