Calculus/Physics Force Problem?
A woman pulls a sled which, together with its load, has a weight of 200 pounds. If her arm makes an angle of x (in radians) with the ground and k is the coefficient of friction (a positive constant), the least force, F, she must exert to move the sled is given by
F(x) = (200x)/ (cos x + k sin x)
Find formula for F’(x) over 0 is < or equal to x which is < or equal to pi/2
I get how to take the derivative but I don't get how to do it over the period [0, pi/2].
Can someone help me with this problem?
Thanks in advance.
There’s nothing special about the period – that’s just the value for x you’d plug into F’(x).
F’(x) = [200 (cos x + k sin x) - 200x (-sin x + k cos x)] / (cos x + k sin x)^2
F’(x) = 200 [(1 - kx) cos x + (k + x) sin x] / (cos x + k sin x)^2
You can plug in values of x between 0<= x <= Pi/2 to get the specific values (note: at x=Pi/2, Force is infinite).
P.S. This equation is incorrect. The force needed to move the sled horizontally at x=Pi/2 should be infinite. The correct equation is:
F(x) = 200k / (cos x + k sin x)
At x = Pi/2, F = 200 (it will start to move UP.)
Here, F'(x) = -200k (-sin x + k cos x) / (cos x + k sin x)^2
2009 European Junior Weightlifting Championships 105+
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