How Does the Work-Energy Theorem Determine the Initial Speed of a Sledgehammer?

[aishax]

Homework Statement

490 J of work is done on a pin when a 5 kg sledgehammer strikes it (bringing the sledgehammer to rest). What is the initial speed of the sledge hammer.

Homework Equations

(Fnet)(d)= (0.5)(m)(velocity final^2 - velocity initial^2)

The Attempt at a Solution

490 = (0.5)(5)(0^2 - v inital^2)
980 = 5 (-v initial^2)
196 = - v initial^2


Problem is, v initial is now negative, and to get rid of the negative, I'd have to divide both sides by -1. But then it would be -196, and I would not be able to square root that. The answer is already given, and it is 14 m/s. It's just that one problem that has me stuck.

Help much appreciated :)

 

[PhanthomJay]

The net force on the pin acts upward, and the displacemnt is downward, so the total work done of 490 J is positive or negative?

 

[aishax]

It would be negative.
But how is the net force on the pin acting upwards?

 

[cepheid]

It would be negative.
But how is the net force on the pin acting upwards?

I think PhantomJay meant that the net force on the hammer is upwards, which is opposite to its displacement (hence the negative work done on the hammer and negative change in its kinetic energy).

 

[aishax]

Ahh, okay. That makes sense.
Thank you! :)

 

[PhanthomJay]

I think PhantomJay meant that the net force on the hammer is upwards

Yes, thanks for the correction.