I only have one more attempt on this question before I lost all of the points, so detailed help would be much appreciated. I understand everything conceptually (I think), but I don't know where I went wrong.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

A 2.3 kg wood block hangs from the bottom of a 1.3 kg, 1.3 meter long rod. The block and rod form a pendulum that swings on a frictionless pivot at the top end of the rod. A 12 g bullet is fired into the block, where it sticks, causing the pendulum to swing out to a 35 degree angle.

2. Relevant equations

Conservation of angular momentum

Conservation of energy

Moment of Inertia

3. The attempt at a solution

m_{b}= .012 kg

m_{B}= 2.3 kg

m_{R}= 1.3 kg

L = 1.3 m

r = .65m

v_{i}= ?

-Conservation of Angular momentum:

A_{i}= A_{f}

A_{i}= (m_{b})(v_{i})(L) = I_{T}(w) = A_{f}

Where w is the final angular velocity

Where I_{T}is the total moment of inertia of the system. Given by:

(1/3)((m_{R})(r)^{2}+ (m_{b}+ m_{B})(L^{2})

So,

1: w =([m_{b}* v_{i}* L)/I_{T}

-Conservation of Energy

KE = Change in PE

KE = (1/2)(I_{T})w_{2}

Change in PE, treating initial position of the pendulum as PE = 0:

PE = m_{T}* g * h

m_{T}is the sum of the masses

Where h is the change in height, denoted by the change in the center of mass as the pendulum rotates:

center of mass = c = (m_{R}* L + (mB + mb)*r)/mT

h = c - c*cos(35)

Equating KE and PE, then solving for w:

w_{2}= (m_{T}* g * h)*2/I_{T}

So w is the square root of all that mess.

Equating the above equation with 1 and solving for v_{i}

v_{i}= (I_{T}* sqrt{ (m_{T}* g * h)*2 / I_{T}}) / ((m_{b})(L))

Which gives me something like 441. I'm really frustrated with this and I'm not sure what I did wrong. Thanks in advance.

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# Homework Help: Angular Momentum (Ballistic Pendulum w/ mass)

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