yes another one if you could?

Question

A 17 g rifle bullet traveling 200 m/s buries itself in a 3.5 kg pendulum hanging on a 2.7 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's displacement.

i'm sorry but both of your answers are wrong. i know this bc the computer gives me feedback. im thinking there is another equation....

Answer 1

mb = 0.017 kg
mp = 3.5 kg
L = 2.7 m

We first need to calculate how fast the bullet/pendulum system is travelling after the collision. This is done through conservation of momentum.

Initially the pendulum is stationary, so it has no momentum.

Pi = Pf

mb * v = (mb + mp)V
.017*200=(.017 + 3.5)V
V = 0.9667 m/s

From here on out we can use energy to solve the rest of the problem. We'll use energy to calculate how high the pendulum goes, then trigonometry to calculate how far the pendulum goes, given a circular arc. Initially, PE = 0, and finally KE = 0.

M = 3.517 (mass of bullet and pendulum)
V = 0.9667 m/s

Ei = Ef
KEi = PEf

½M V² = Mgh
M's cancel

.5 * .9667² = 9.8 * h

h = .0477 m


Well, that actually answers the first question. The vertical displacement is 0.0477m. Now we need to figure out the horizontal displacement.


We know the radius of the circle is 2.7m. Draw a right triangle.

The hypotenuse is 2.7. The vertical leg is .0477. The horizontal leg is the one we want. Pythagorean to the resuce.

x² + .0477² = 2.7²
x = 2.70 m




When working through physics, here are some questions you should ask.

Is there a collision?
If yes, then does momentum apply?

Am I trying to calculate speed or height?
If yes, then how does energy fit into the problem?

Do I have enough information to draw a free body diagram, or am I given information about forces?
If yes, then how can I apply F=ma?

Answer 2

I'd say use Energy, all kinetic energy at first, then it becomes all grav. potential

1/2 m v^2 = (m + m) gh

the first m, is the bullet, the second is the bullet plus the wood, I hope thats right; it would be the vertical disp.

(.017)(200^2)
------------------------------
(2)(.017 + 3.5) ( 9.8)

after that, just draw a triangle, the hypotenuse would be 2.7, and the height would be whatever you got in the first part. use trig... uhoh whats the angle...crap, i'm sorry hopefully someone else got it, i might edit later if I get it

EDIT:

wow! ok my bad, i'm just ridiculously dumb right now. Draw a right triangle, the hypotenuse is 2.7, the height is (2.7 - .09864) btw I solved the above for the vertical displacment, .09864, use pythagorean theorum to find the remaining leg of the triangle,

horizontal leg is .72315 I believe, re-check my work!