## Monday, February 15, 2010

### A Whale of a Time

Fox once aired a show called Man vs. Beast, featuring several of nature's greatest rivalries: world class sprinter Shawn Crawford vs. a zebra, hot dog eating champion Takeru Kobayashi vs. a Kodiak bear, and—my personal favorite—a team of little people competing with an elephant to pull a DC-10 airliner. This type of quality programming inspires mathematical minds. What other great match-ups could we have? For example, how many musclemen would it take to hold back a whale?

Balaenoptera musculus, the blue whale, averages 150 tons (1.5×105 kg) and can reach a top speed of about 31 mph, which is roughly 14 m/s.  Assuming it takes 10 seconds to reach top speed, we can calculate the force the whale uses to accelerate itself using the formula,

force = (mass) · (change in velocity) / (change in time)
= (1.5×105 kg) · (14 m/s) / (10 s)
= 2.1×105 N.

Here, “N” is short for “Newton”, a unit of force. The musclemen would need to exert an equal and opposite force on the whale to hold him back. In the gym, it’s common to see some of the bigger men doing lateral rows with 200 lbs, which corresponds to 980 N.

From this we can calculate how many musclemen we’d need to hold back a whale,

number of musclemen = (force per whale) / (force per muscle man)
= (2.1×105 N per whale) / (980 N per muscle man)
= 214 musclemen per whale.

It would take over 200 fairly strong people to hold back a whale. Check out Diary of Numbers tomorrow, as we’ll have a question from a special guest!