Projectiles ability to do work to a box when connected by string? I was wondering, the work-energy theorem states that KE can do work, as it is Mechanical energy.
if the KE energy and thus Mechanical energy of a ball, if external...can do work on an object, applying force. 
so, If I have a ball with a string attached to it with a box, some KE is lost in deformation and such but the ball extends out and pulls the box, doing work on the box.
I know a hammer hits in a nail with Kinetic energy, which is mechanical energy, I know that external forces do work, so like a bullet has the ability to do work and can do so but it penetrates and exerts force inside object, it doesn't do work as its energy is taken up in deformation and such...but if a bullet does penetrate inside the body and then still exerts a force without losing KE to deformation, it could do work and such but that doesn't happen as bullets usually deform or lose all energy, the deformations is the material doing work on the bullet but the bullet doing work on the material creative a cavity by the exerted/transferred force, the time it lasts isn't very long and it creates a cavity for a short time as the force is applied for a short time. 
though we digress, if a bullet attached by string could do work pulling a box to which its connected to, correct?
 A: 
though we digress, if a bullet attached by string could do work pulling a box to which its connected to, correct?

Of course, when the bullet is connected to a box which was initially at rest the box will start moving as soon as the string is strained tight. While the box accelerates, the bullet decelerates. 
The same force acts on both, you divide through each's mass to get the corresponding acceleration and deceleration. While the boxes velocity increases from 0 to its final value the box accelerates. 
Since it accelerates for a distance greater than zero, the boxes mass times the acceleration times the distance it accelerates gives you the kinetic energy of the box, or in other words the work the bullet did to the box. 
If the bullet is to fast it might tear the string or break material of the box since the destruction factor depends mostly on velocity (therefore light but fast bullets for penetration), but the same principles will still hold, you then just substract the energy that was used to break the material of the box and divide through the mass of the remaining part of the box that is still attached to the string to get your acceleration:deceleration-ratio of the box and the bullet. 
If you remember that energy and momentum are conserved it is easy to calculate the final velocity of the bullet and the box if you know their mass (with air resistance it is a bit more complicated).
