# 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  6 ms^-2?

May 7, 2016

$F = {F}_{\text{frict"+F_"accel}} = 196 + 30 = 226$ $N$

#### Explanation:

The total force required will be given by $F = {F}_{\text{frict"+F_"accel}}$ - the sum of the force required to overcome friction and the force required to accelerate the mass.

The frictional force is given by:

${F}_{\text{frict"=muF_"norm}}$ where the normal force ${F}_{\text{norm}} = m g$

So the friction force is ${F}_{\text{frict}} = \mu m g = 4 \times 5 \times 9.8 = 196$ $N$

To accelerate a mass the force given by Newton's Second Law is:

${F}_{\text{accel}} = m a = 5 \times 6 = 30$ $N$

Then:

$F = {F}_{\text{frict"+F_"accel}} = 196 + 30 = 226$ $N$