# Homework Help: Energy stored in a bow and arrow

1. Dec 19, 2008

### vectordog

The following was a question from a Work/Energy high school test.
"3. An archer is shooting at a hay bale target. The archer pulls back on his bow string with 500 N of force to draw it back a distance of 80 cm. He releases the string, and the arrow (m= 1 Kg) flies straight to its target (neglect air resistance).
a) How fast is the arrow traveling when it leaves the bow?"
Some students used the work-energy theorem (W=delta KE in this case) and got an answer of 28.3 m/s. However, many students used the info given to determine a spring constant (k) for the bow (k = F/x), and then applied Conservation of Energy (Elastic PE = KE in this case) to the system. This yields an answer of 20 m/s for the arrow.
My question is "Why doesn't the spring constant method work?"

2. Dec 19, 2008

### Staff: Mentor

They messed up.
That's fine.
Both methods, done correctly, yield the same answer. Note that the spring force varies from 500 N at first to zero at the release. You can't just use W=Fx = 500*0.8.

3. Dec 19, 2008

### vectordog

THANKS!!!
I feel a little stupid now.