This is my first post on here; I hope it will be worth it. I haven't been able to find an adequate solution to this elsewhere.(adsbygoogle = window.adsbygoogle || []).push({});

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

A 5.30 kg ball is dropped from a height of 11.5 m above one end of a uniform bar that pivots at its center. The bar has mass 8.50 kg and is 9.00 m in length. At the other end of the bar sits another 5.40 kg ball, unattached to the bar. The dropped ball sticks to the bar after the collision.

2. Relevant equations

[itex]W_t=K_t[/itex]

[itex]L_i=L_f[/itex]

[itex]L=mvr[/itex]

[itex]v=r\omega[/itex]

3. The attempt at a solution

First, I defined the data given as following:

[itex]m_1 = 5.3kg, h_1 = 11.5 m, m_b = 8.5 kg, \ell = 9.00m, m_2 = 5.4kg[/itex]

Then, I looked up the moments of inertia for the bar and balls relative to the center of the bar, then found the total of these:

[itex]I_b=\frac{1}{12}m_b(\frac{\ell}{2})^2=8.94 kg \, m^2[/itex]

[itex]I_1=m_1(\frac{\ell}{2})^2=107 kg \, m^2[/itex]

[itex]I_2=m_2(\frac{\ell}{2})^2=109 kg \, m^2[/itex]

[itex]I_t=\sum I = 225.6 kg \, m^2[/itex]

Then, I found the resulting velocity of the 1st ball when it hits the bar:

[itex]m_1h_1g = I_2\omega_2^2 \implies v = \sqrt{2h_1g} \implies v = 15 \frac{m}{s}[/itex]

Then I used the conservation of angular momentum to find the final angular velocity after the bar has rotated:

[itex]L_1 = m_1v_1\frac{\ell}{2}=357.75Nms[/itex]

[itex]L_2=I_t\omega[/itex]

[itex]L_1=L_2 \implies I_t\omega = L_1 \implies \omega = \frac{L_1}{I_t} = 1.59 \frac{rad}{sec}[/itex]

Then I found the initial velocity of the ball moving upwards from the angular velocity and used the work energy theorem to find the final height of the ball.

[itex]v=\frac{\ell}{2} \omega \implies v=7.14 \frac{m}{s}[/itex]

[itex]\frac{1}{2}m_2v^2=m_2gh_2 \implies h_2=\frac{v^2}{2g} \implies h_2 = 2.60 m[/itex]

However, this is the incorrect value for [itex]h_2[/itex]. Any ideas?

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# Homework Help: Mastering Physics 10.85 - Dynamics of Rotational Motion

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