Ballistic Pendulum Homework Problem

[freshpulp]

I'm having trouble with this physics question:

A 20kg sphere is hanging from a hook by a thin wire 3.50m long, and can swing in a complete circle. It is struck horizontally by a 5kg steel dart that embeds itself in the sphere. What is the minimum speed of the dart such that on contact it causes the combination to make one circular loop?

This seems very much like a ballistic pendulum question but I can't seem to get the correct answer. I assumed that if the pendulum managed to reach the apex of its trajectory (in which it would be diametrically opposite from the rest point), then the force of gravity would bring it back, completing the circle. That didn't work. What am I doing wrong?

The ballistic pendulum equation, by the way, is v=(m+M/m)sqrt(2gy), where m is the mass of the moving dart and M the mass of the motionless sphere.

 

[Doc Al]

Originally posted by freshpulp
This seems very much like a ballistic pendulum question but I can't seem to get the correct answer. I assumed that if the pendulum managed to reach the apex of its trajectory (in which it would be diametrically opposite from the rest point), then the force of gravity would bring it back, completing the circle. That didn't work. What am I doing wrong?

Assuming the wire is flexible, you need to ensure that tension is maintained throughout the motion. Start by finding the minimum KE that the system (sphere + dart) must have at the top of the motion to maintain a slight bit of tension in the wire. Hint: it's not zero.

 

[turin]

Originally posted by Doc Al
Assuming the wire is flexible, you need to ensure that tension is maintained throughout the motion.

Wow. I don't think I ever would have thought of that. That's one of the main reasons why I browse these forums. Thanks Doc Al.