# An object with a mass of 12 kg is on a surface with a kinetic friction coefficient of  15 . How much force is necessary to accelerate the object horizontally at  1 m/s^2?

Jun 8, 2018

The force is $= 1776 N$

#### Explanation:

The acceleration is $a = 1 m {s}^{-} 2$

The mass of the object is $m = 12 k g$

Apply Newton's Second Law to calculate the force

$F - {F}_{r} = m \cdot a = 12 \cdot 1 = 12 N$

The acceleration due to gravity is $g = 9.8 m {s}^{-} 2$

The normal force (reaction) is $N = m g = 12 \cdot 9.8 = 117.6 N$

The coefficient of kinetic friction is ${\mu}_{k} = 15$

The frictional force is

${F}_{r} = N {\mu}_{k} = 117.6 \cdot 15 = = 1764$

The force is

$F = 12 + {F}_{r} = 12 + 1764 = 1776 N$