Basic Equations (1) – Rocking the boat

Here’s a picture of a rower, just to explain the basic concepts. Click on the image to see a full size version. The system consists of a crew with its mass m_c and a boat with its mass m_b.

The entire system is moving with a velocity v_t with respect to the viewer on the dock. However, the crew is moving with respect to the boat, and as a consequence (conservation of momentum) the boat itself moves at a higher speed v_t + v_b. The crew velocity is v_t + v_b - v_c.

Conservation of momentum gives us:

m_c (v_t + v_b - v_c) + m_b (v_t + v_b) = m_c v_t + m_b v_t

So, we can derive what you do to your shell speed by racing the recovery:

v_b = \frac{m_c}{m_c + m_b} v_c

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2 thoughts on “Basic Equations (1) – Rocking the boat

  1. sanderroosendaal Post author

    Thanks. I feel impressed and honored. Atkinson, Van Holst and Kleshnev responding on my blog within a few days of opening.

    I’d love to see your future comments on this blog. I read your papers and the work of Atkinson and Van Holst, and am using of lot of it in my calculations. I added a reference to your site on the first post.

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