Question

An object with a mass of `15 kg` is moving at `9 m/s` over a surface with a kinetic friction coefficient of `4`. How much power will it take to accelerate the object at #3 m/s^2?

Answer 1

Frictional force acting on the object is `fk`= `u* N` or, umg i.e 600 N,
So, let's assume we will be requiring a force of F to accelerate the object at 3 `(m/sec^2)`
So,using equation of force we can write,
`(F - fk)` = `ma`
Or, F = `(15*3)`+600 N i.e 645 N
Now,if this force cause displacement s of the object wi th in time t,power will be (work done/time) i.e 645`(s/t)`

Answer 2

The power is `=5.697kW`

Explanation:

The mass of the object is `m=15kg`

The speed is `u=9ms^-1`

The acceleration is `a=3ms^-2`

The coefficient of kinetic friction is

`mu_k=F_r/N=4`

The normal force is `N=15gN`

The frictional force is `F_r=mu_k xx N=4*15g=60gN`

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=((15xx3)+(60g))N=633N`

`"Power"="Force"xx "velocity"`

The power is

`P=Fxxv=633*9=5697W`