A 14 g rifle bullet traveling 210 m/s buries itself in a 3.9 kg pendulum hanging on a 2.6 m long string, which makes the pendulum swing upward in an arc. Determine the horizontal component of the pendulum's displacement (m)
2006-08-01 02:02:03 · 6 answers · asked by leila_davies1986 1 in Science & Mathematics ➔ Physics
If you assume this to be perfectly elastic...
That is, all of the bullet's momentum is transferred to the pendulum, you know exactly how much energy is transferred to the pendulum...
ie.
p(bullet) = mv = .014*210 = 2.94 kg*m/s
so, in a collsion
p(bullet) = (m(bullet)+m(pend))*v(both) = 4.04*v(both)
so v0(both) (in the x-direction) = .728 m/s
You can assume that the kinetic energy of the bullet is transferred completely into the pendulum,
thus,
m(both)gh = .5*m(both)*v(both)^2
h = .5*v(both)^2/g ... so now you have its vertical displacement (initial)
you have the length of the string...
so you know the distance from the connetion point of the string down... and the length of the string...
use pythag to get the horizontal displacement...
where, a = length of string - vertical displacement
b = length of string
c = horizontal displacement
c = sqrt(a^2 + b^2)
there you have it
2006-08-01 02:13:42 · answer #1 · answered by AresIV 4 · 0⤊ 0⤋
Use conservation of energy. Work out the kinetic energy of the bullet. Convert that into potential energy of the combined mass of the bullet and the pendulum which will tell you how high it has to rise to convert all the kinetic into potential energy.
Now you have got the height the pendulum bob has risen (lets call it H), you have now got a simple triangle to solve. The hypotenuse is 2.6m, the vertical is (2.6-H)m so you can easily solve the horizontal component as it's a right angled triangle.
2006-08-01 02:14:05 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Ok, I did this experiment before (no not with a real gun, but a projectile that moved pretty fast).
First do that m1v1 + m2v2 = m1v1 + m2v2 thing.
With that, you'll have the initial velocity of the pendulum. Then you determine how high it will go (using KE and PE formulas). Remember to use gravity and centripetal acceleration. Good luck!
2006-08-01 02:07:48 · answer #3 · answered by M 4 · 0⤊ 0⤋
OK. I just figured it out. Now what should I do?
2006-08-01 02:05:56 · answer #4 · answered by Anonymous · 0⤊ 0⤋
get books
2006-08-01 02:07:12 · answer #5 · answered by Anonymous · 0⤊ 1⤋
Solved it...............
2006-08-01 02:17:56 · answer #6 · answered by ag_iitkgp 7 · 0⤊ 1⤋