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Old Nov 6th 2009, 05:52 PM   #1
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Finding Initial Velocity

A student performs a ballistic pendulum
experiment using an apparatus similar to that
shown in the figure.
Initially the bullet is fired at the block while
the block is at rest (at its lowest swing point).
After the bullet hits the block, the block rises
to its highest position, see dashed block in the
figure, and continues swinging back and forth.
The following data is obtained:
the maximum height the pendulum rises is
4 cm,
at the maximum height the pendulum sub-
tends an angle of 42.8◦,
the mass of the bullet is 66 g, and
the mass of the pendulum bob is 874 g.
The acceleration of gravity is 9.8 m/s2 .
874 g
66 g vi vf
42.8◦
4 cm
Determine the initial speed of the projec-
tile.
Answer in units of m/s.
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Old Nov 7th 2009, 10:09 AM   #2
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This looks a complicated question, because too much data was provided! but if you focus on the question it's easy.

Assuming no friction:

The pendulum has a mass of 874g and rises 4cm from the horizontal.
The bullets mass is 66g.

PE = mgh = 0.874*9.8*0.04 = 0.3426 J

PE transferred = kinetic energy

KE= (1/2)mv^2

0.3426/(1/2)m = v^2

I'll leave the rest to you.

this is the answer your aiming for:
Spoiler:
3.222 m/s
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Old Nov 7th 2009, 11:45 AM   #3
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From what i remember, in a ballistics pendulum the bullet gets embedded in the block so the collision has to be treated as inelastic i.e. K.E. will not be conserved. However, momentum is conserved. Hence,

66 x Vbullet = (66 + 874) V(bullet + block) ......(1)

Since the bullet + block system is raised thru 4 cm,

(66+874) g 4 = 0.5 (66+874) V(bullet+block)^2 .....(2)

Solve 2 to get V(bullet+block). Plug this value back into (1) and get Vbullet
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Old Nov 7th 2009, 11:54 AM   #4
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Where in the question does it say the bullet sticks in the block?
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Old Nov 7th 2009, 12:45 PM   #5
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it did stick, me and my friend figured it out last night, it ended up being 12.6, thank you for your answers
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Old Nov 7th 2009, 11:51 PM   #6
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It doesnt say so specifically but ballisitcs pendulums are used to study bullets and the typical procedure is such that it sticks.
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