Question

What force is needed to give a 0.25-kg arrow an acceleration of 196 m/s squared?

Answer 1

`F=49"N"`

Explanation:

We can apply Newton's second law here, which in summary states that the acceleration underwent by an object is directly proportional to--and in the same direction as--the net force experienced by the object.

We know this as the familiar equation: `color(blue)(vecF=mveca)`.

Given:

• `m=0.25"kg"`
• `a=196"m"//"s"^2`

With this information we can calculate the force required to cause the given acceleration with the given mass constraint.

Note that I am assuming that this arrow is shot horizontally, where the applied force--and consequently the given acceleration of the arrow--is entirely in the x-direction. I also make the usual assumptions for projectile motion at this level: air resistance is negligible, ignore the curvature of the earth, etc.

Of course the arrow also undergoes a vertical acceleration equal to `-g`, or the free-fall acceleration, so again, I assume the desired acceleration is meant to be entirely horizontal and otherwise unaffected by the force of gravity.

Then:

`F=ma`

`=>=(0.25"kg")(196"m"//"s"^2)`

`=>=color(blue)(49"N")`