# 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  7 m/s^2?

Feb 19, 2017

231 Newtons

#### Explanation:

Newton's Law

${F}_{\text{net}} = m a$

${F}_{\text{applied" - F_"friction}} = m a$

Friction equation where u is the coefficient of friction

${F}_{\text{applied" - uF_"normal}} = m a$

The magnitude of normal force is equal to the force of gravity

${F}_{\text{applied}} - u m g = m a$

${F}_{\text{applied}} = m a + u m g$

Plugging in numbers

$= 5 \cdot 7 + 4 \cdot 5 \cdot 9.8$

$= 231$ Newtons of force that needs to be applied