Question

An object with a mass of `7 kg` is on a surface with a kinetic friction coefficient of `8`. How much force is necessary to accelerate the object horizontally at `32 m/s^2`?

Answer 1

`784 N`

Explanation:

As,the object is going on a horizontal surface,frictional force acting on it will be `f = u*N` or `umg` i.e `(8*7*10`) N or, 560 N

So,le't's assume we will be requiring a force of F to cause an acceleration of 32 SI units on it.

so,we can write, `F-f = m*a`(where, m is the mass of the object and a is its acceleration)

so, `F=(560+7*32)` N or, `784 N`

Answer 2

The force is `=772.8N`

Explanation:

The mass of the object is `m=7kg`

The acceleration is `a=32ms^-2`

The coefficient of kinetic friction is

`mu_k=F_r/N=8`

The normal force is `N=7gN`

The frictional force is `F_r=mu_k xx N=8*7g=56gN`

The force necessary to accelerate the object is `=FN`

The acceleration due to gravity is `g=9.8ms^-2`

According to Newton's Second Law

`F-F_r=ma`

`F=ma+F_r=((7xx32)+(56g))N=772.8N`