I am reviewing my calculus (it has been many years). Hope this is ok to ask, amongst all the young'ins...(adsbygoogle = window.adsbygoogle || []).push({});

I was doing fine until:

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

1) A mass M is drawn up a straight incline of given height h by a mass m which is attached to the first mass by a string passing from it over a pulley at the top of the incline and which hangs vertically. Find the angle of the incline in order that the time of ascent be a minimum.

2) A swinging pendulum is 4 feet long is rotating at the rate of 18 deg/sec when it makes an angle of 30 with the vertical. How fast is the end of the pendulum rising or falling at that moment.

2. Relevant equations

F=ma, trig functions

3. The attempt at a solution

For 1, I calculated the net force on M as Ma = 32m - 32 M sin A. Reasoning that the greatest acceleration would also make the least time, I do:

a = 32m/M - 32 sin A.

I just treat this as a derivative (which it is), and set it to zero, solving for sin A:

sin A = m/M

However, the book (Morris Kline's calculus) gives sin A = m/2M.

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For 2, the pendulum is sweeping out a circle, so s = rA, where a is the angle with the vertical. Differentiating, I get ds/dt = r dA/dt. From the problem data, r = 4 ft, dA/dt = 18 deg/sec = pi /10 rad/sec. ds/dt is v, the velocity, so the answer should be 4 (pi/10) = 2*pi/5 ft/sec. But the answer in the book is pi/5 ft/sec.

I thought perhaps they might want the vertical speed. For that I get vy = v/sin 30 = 2v = 4*pi/5 ft/sec. Even farther away.

Any help you can give to help this old guy keep his brain alive would be appreciated.

Thank you,

Sheldon

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

2. Relevant equations

3. The attempt at a solution

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# Two Simple Problems

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