An object with a mass of 5 kg is on a surface with a kinetic friction coefficient of  4 . How much force is necessary to accelerate the object horizontally at 1 m/s^2?

Dec 25, 2017

The force is $= 201 N$

Explanation:

The mass of the object is $m = 5 k g$

The acceleration is $a = 8 m {s}^{-} 2$

The coefficient of kinetic friction is

${\mu}_{k} = {F}_{r} / N = 4$

The normal force is $N = 5 g N$

The frictional force is ${F}_{r} = {\mu}_{k} \times N = 4 \cdot 5 g = 20 g N$

The force necessary to accelerate the object is $= F N$

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

The acceleration of the object is $a = 1 m {s}^{-} 1$

According to Newton's Second Law

$F - {F}_{r} = m a$

$F = m a + {F}_{r} = \left(\left(5 \times 1\right) + \left(20 g\right)\right) N = 201 N$