"Calculating the Velocity of an Arrow Hitting Hay

[lking226]

Homework Statement

A 1kg arrow hits a bail of hay and penetrates 47.0cm. The average frictional force of the hay on the arrow is 2500.0N. What was the original velocity of the arrow?

Homework Equations

Ffr = uk x Fn

The Attempt at a Solution

I'm completely lost, can someone please walk me through this?

 

[jegues]

Well we know that,

W = fdcos(theta).

cos(theta) is going to go to 1 so,

W = fd.

We're given then average force and the distance so we can solve for the work done.

After you've done that I want you to think about the kinetic energy - work theorem ;)

 

[lking226]

is the kinetic energy-work theorem net work = change in kinetic energy?
so then, w = 1/2mvf^2-1/2mvi^2, but vf is 0 because the arrow is stopped in the hay so really w = -1/2mvi^2. does that stay negative?

 

[cepheid]

is the kinetic energy-work theorem net work = change in kinetic energy?
so then, w = 1/2mvf^2-1/2mvi^2, but vf is 0 because the arrow is stopped in the hay so really w = -1/2mvi^2. does that stay negative?

Yes, the work done is negative, because the kinetic energy decreaes (in this case all the way to zero, so that the change in kinetic energy is just the negative of how much there was to start with).

 

[lking226]

got it, thanks guys!