Question

An object with a mass of `2 kg` is moving at `7 m/s` over a surface with a kinetic friction coefficient of `1`. How much power will it take to accelerate the object at #4 m/s^2?

Answer 1

The power that much be supplied at the moment `v=7m/s` is `193.2 W`

Explanation:

The power expended on an object can be found by multiplying the force applied to the object by the speed of the object's motion.

`P=Fxxv`

To cause acceleration of `4m/s^2` we require a net force of

`F_"net"=ma = (2kg)(4m/s^2)=8 N`

Since there is a frictional force present, this net force is composed of two separate forces

`vecF_"net"= vecF_"applied"+vecF_f`

where the force of friction will equal `mumg`, and `mu = 1`

So,

`8N = F_"applied" - (2)(9.8)`

"F_"applied"= 8 + 19.6 = 27.6N#

At the moment the acceleration begins, `v=7m/s`, and the power expended is

`P=F_"appied" xx v=(27.6N)(7m/s)= 193.2W`

Note that as the speed increases, the power required to maintain this acceleration will increase, so the above answer is true only at the moment v = 7 m/s.