Pendulum conservation of momentum

[bcjochim07]

Homework Statement

A 20 kg wood ball hangs from 2m long wire. The maximum tension the wire can withstand without breaking is 400N. A 1 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the largest speed this projectile can have with causing the wire to break?

Homework Equations

The Attempt at a Solution

I first used conservation of momentum

vop= initial velocity of projectile

(1kg)(vop)=(21kg)(vf)

Then I tried drawing a force body diagram. Then the thought occurred to me that not only tension acts in the radial direction, but also gravity once the pendulum swings out to an angle. So isn't momentum only conserved right before and right after the collision?
Any hints would be greatly appreciated.

 

[Oomair]

ok here are my assumptions,

1. i think the problem wants us to assume that there is no angle made from the vertical, thus eliminating an integration factor

2. 1kg Vo= 21kg Vf

3. You can use energy, and apply your results to a free body diagram

 

[Oomair]

and Vf = (Vo)/21kg,

 

[tiny-tim]

So isn't momentum only conserved right before and right after the collision?

Hi bcjochim07!

That's right … at the collision itself, the change in momentum is impulsive (ie sudden), so the gradual forces (weight and tension) can be ignored.

After that, you do have to include both weight and tension, as you say.

Hint: first calculate the tension when the string is vertical (because that's the easy case … you can do it for the string at an angle later).

And that tension is … ?

 

[bcjochim07]

tension when it is vertical is 205.8 N. So when it is at angle, the force of gravity along the radial direction will be less.

So if I can ignore the angle like oomair says:
so vf=vpo/21kg

So you're saying that i should say
F= (400N)= (21kg)*(vpo/21)^2/(2m)
and solve for vpo??

Is these an ok assumption??

 

[tiny-tim]

F= (400N)= (21kg)*(vpo/21)^2/(2m)

Not quite … you've put tension = mass x acceleration … but you have to include the weight (the gravitational force)!

 

[bcjochim07]

oh ok include the weight that I calculated when it is vertical in the sum of forces with the 400 N and then solve for vpo. I think I've got it.

 

[tiny-tim]

That's it!

And don't forget to comment on whether the tension is a maximum in the vertical position!

( … if aok now, don't forget to click on "Thread Tools" to mark the thread [SOLVED] … )​