Calculating Maximum Displacement of Pendulum from Ballistic Impact

[Oomair]

[SOLVED] Ballistic pendelum problem

Homework Statement

16 g rifle bullet traveling 180 m/s buries itself in a 4.0 kg pendulum hanging on a 3.5 m long string, which makes the pendulum swing upward in an arc. Determine the horizontal component of the pendulum's maximum displacement

Homework Equations

arc length s= rtheta

The Attempt at a Solution

i don't think the block and bullet make a angle with a vertical
so work= F*s where S= Rtheta, but i can't find theta,

 

[tiny-tim]

Hi Oomair!

Energy isn't conserved in the collision (you know that because the question tells you that the bullet "buries itself" in the pendulum).

So use conservation of momentum to find the initial speed of the pendulum.

Then find its maximum height by … ?

 

[Oomair]

ok i found the max height which came out to be .0262 meters, but its wants the horizontal displacement, i don't know how to relate the height to the horizontal displacement,

since its displacement is like an arc, so S= rtheta, so this is where I am stuck, i have tried freebody diagrams and even used integration,

 

[tiny-tim]

Hi Oomair!

Yes, .0262m looks right.

ok, the rest is just geometry.

Horizontal displacement just means the sideways component of distance.

So draw a triangle. The hypotenuse is 3.5. One side is 3.5 minus .0262. So the third side is … ?

 

[Oomair]

thanks, that worked, i didnt know that the hypotenuse could be the length of the string, what a weird problem lol