Motion System Design
Fun with Fundamentals: Problem 169

Fun with Fundamentals: Problem 169

Bank shot and Solution to Problem 168. Money is the root of all fine print, as this month's problem by Walter Jasiolek of Northville, Mich., demonstrates

Bank shot

Problem 169 — Money is the root of all fine print, as this month’s problem by Walter Jasiolek of Northville, Mich., demonstrates

“Fellow employees,” intoned T. Bone More, president of the More Bank & Trust, “I’ve come all the way from my office to this meeting room to explain our new loan program, the Strategic Equity New-model Draft program or SEND.

“The loan period is one year,” continued More. “Our logo is this:


“The computer program that calculates the interest is configured so that SEND is the principal borrowed by the customer, MORE is the interest we charge,” chuckled More, “and MONEY is what the customer pays back.”

If each letter of the letter represents a unique, whole number between 0 and 9, inclusive, and “M” ≠ 0, what is the principal, interest, and total amount?

Send your answer to:
Fun With Fundamentals
1100 Superior Ave.
Cleveland, OH 44114-2543

Technical consultant: Jack Couillard, Menasha, Wis.

Solution to last month’s problem 168 — You rarely go around in circles if you answered 43.6 mph.. Here’s how Bluff got “up to speed.”

For the system to be in equilibrium, each time Wurme and the boat make a revolution, Bluff and the inner tube must also make a revolution.

Recognizing this, the basic equation for angular velocity is:

v = r ω


v = linear velocity of boat, given as 20 mph

ω = angular velocity, radians per sec r = radius of circle traveled by boat, given as 50 ft.

Since ω is a constant, all we need is the inner tube’s radius to solve for its velocity. Using trigonometry:

b = 75 ft x sin 30 = 37.5 ft
= 75 ft 3cos 30 = 64.95 ft

Using the formula for a right triangle:

The inner tube’s velocity is then:

Wurme still knows all the angles!

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