Balistic Pendulum Equation Solution

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An 8.0g bullet embedded in a 2.5kg block of wood swings to a height of 6.0cm after impact, leading to several calculations. The potential energy (PE) at the top is calculated as 1.47 J, which some participants question for its reasonableness. The kinetic energy (KE) at the bottom is derived from conservation of energy principles, with the velocity immediately after impact calculated to be approximately 1.08 m/s. Momentum at the bottom is determined to be 2.71 kg·m/s, and the initial speed of the bullet is estimated at 339 m/s, deemed reasonable for a bullet. The discussion emphasizes the importance of precise equations and proper identification of initial and final states in energy calculations.
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Homework Statement


An 8.0g bullet is fired into and becomes embedded in a 2.5kg block of wood at the end of a pendulum. The block of wood swing to a height of 6.0cm. (Watch Units)
a) What is the PE of the block & bullet at the top?
b) What is the KE at the bottom? (COE)
c) What is the velocity of the block & bullet right after the impact?
d) What is the pmomentum at the bottom?
e) What was the initial speed of the bullet? (COM)

Homework Equations


KE= PE
KE= 1/2 mv2
PE= mgh
P=mv
m1v1+m2v2=(m1+m2)v'

The Attempt at a Solution


a)PE = (.008kg + 2.5kg)(9.8 m/s2)(.06m) = 1.47 J (doesnt seem like a reasonable number to me)

b)KE = .5(.008kg + 2.5kg)(v)2

c) mgh=1/2mv2

2gh=v2
v=(square root)2gh
(square root) (2)(9.8m/s2)(.06m)=1.08 m/s

d)Does "bottom" mean not moving? if not, then
P=mv P=(.008kg+2.5kg)(1.08m/s)=2.71 kgm/s

e)(.008kg)(v1) + (2.5kg)(v2) = (.008kg + 2.5kg)v'
.008kg(v1) + 2.5kg(v2) = 2.508kg(v')
 
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figured it out
 
EDIT: I was in the process of typing this up while you figured it out. You may still find my first comment useful, though.

Woopy said:

Homework Statement


An 8.0g bullet is fired into and becomes embedded in a 2.5kg block of wood at the end of a pendulum. The block of wood swing to a height of 6.0cm. (Watch Units)
a) What is the PE of the block & bullet at the top?
b) What is the KE at the bottom? (COE)
c) What is the velocity of the block & bullet right after the impact?
d) What is the pmomentum at the bottom?
e) What was the initial speed of the bullet? (COM)

Homework Equations


KE= PE
This is too vague (i.e. generally untrue). I would advise against ever using this equation because it is imprecise and can cause confusion. I suggest the more explicit:

KEi+PEi=KEf+PEf

from which you can derive

KEi=PEf

by recognizing that KEf=0 (at the top of the swinging motion of the block) and PEi=0 (by simply choosing that as your zero point for PE, since gravitational PE is relative to your choice of zero).
Notice that the KE in this equation corresponds to a different situation than the PE, which I have indicated with the identifiers, "i" for initial and "f" for final.

Alternatively, try:

KEi+PEi=KEf+PEf
=>
KEi-KEf=PEf-PEi
=>
KEi=ΔPE
(is KEf=0)



Woopy said:
a)PE = (.008kg + 2.5kg)(9.8 m/s2)(.06m) = 1.47 J (doesnt seem like a reasonable number to me)
Why does this seem unreasonable to you? I got the same thing, except for a sig fig issue. If you need to be picky about sig figs, then how many should you have?



Woopy said:
b)KE = .5(.008kg + 2.5kg)(v)2
No. Use the hint, "(COE)". This is basically how you solved part (c), so you obviously know how to do this. Think of part (b) as an intermediate step between parts (a) and (c); I think that was the point of part (b).



Woopy said:
d)Does "bottom" mean not moving?
Probably so, since it specifies "after the impact".



Woopy said:
e)(.008kg)(v1) + (2.5kg)(v2) = (.008kg + 2.5kg)v'
.008kg(v1) + 2.5kg(v2) = 2.508kg(v')
Any guesses what is v2 and v'?
 
would PE be KE also, as part b as 1.47 J?

and for part e I ended up getting 339 m/s, which seems reasonable for a bullet
 
Woopy said:
would PE be KE also, as part b as 1.47 J?
Yes. And it looks like you're doing fine with these problems, but I still strongly suggest that you take heed of my first suggestion in my previous post. (That includes the use of more specific identification, such as "i" and "f".)



Woopy said:
... for part e I ended up getting 339 m/s, which seems reasonable for a bullet
It seems reasonable to me, too. :)
 
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