Question

The acceleration of a sled is `2"m"//"s"^2`. What is the acceleration of the sled if we triple the net force and halve the mass?

Answer 1

`a=12" m"//"s"^2`

Explanation:

By Newton's second law, we can state that the acceleration experienced by an object is proportional to the net force acting on it:

`color(blue)(vecF_("net")=mveca)`

We are given that `a=2" m"//"s"^2`

`=>F=(2" m"//"s"^2)*m`

Therefore we can solve for acceleration and write:

`=>2" m"//"s"^2=F/m`

We want to know what happens to the acceleration of the sled if we triple the net force `F` and halve the mass `m`. Let's see how this would affect the right side of the equation.

`F/m`

`=>(3F)/(1/2m)`

`=>(6F)/m`

`=>6(F/m)`

So we can see that tripling `F` and halving `m` will lead to a net force which is six times greater than before. Hence, we have:

`a=6*(2" m"//"s"^2)`

`=color(blue)(12" m"//"s"^2)`