The weight in the weight pan stretches the cable and produces a tensile force F
ID: 1848394 • Letter: T
Question
The weight in the weight pan stretches the cable and produces a tensile force F in the cable. This force is transmitted to the person's hand through the handle. The force makes an angle theta with the horizontal and applied to the hand at B. Point A represents the center of gravity of the person's lower arm and O is a point along the center of rotation of the elbow joint Assume that points O, A, and B and force F all lie on a plane surface. If the horizontal distance between O and A is a = 15 cm, distance between O and B is b=35 cm, total weight of the lower arm is W = 20 N, magnitude of the applied force is F = 50 N, and angle theta = 30degree, determine the net moment generated about O by F and W.Explanation / Answer
The probability density function (continuous variable) or the probability mass function (discrete variable) of a random variable X contains all the information you'll ever need about this variable. Therefore, it seems that it should always be possible: * to calculate the mean, variance and higher order moments of X from its p.d.f. (or its discrete p.m.f.). * to calculate the distribution of, say, the sum of two independent random variables X and Y whose distributions are known. Yet, in practice, it turns out that calculations from first principles are often intractable. The Moment Generating Function (mgf) may then come to our help. Before we describe the mgf, a little digression is in order. The difficulty we just mentioned is not specific to Probability Theory. In fact, just about any disciplin in Physics or Mathematics will run into the same problem sooner or later: a certain property of a function f is needed, the equations are there, but cannot be solved in a closed form. A very powerful and general idea, that exists under many guises, consists then in transforming the original function f into a new and appropriately chosen function g, such that comparatively simple calculations on g will provide the desired results. The obstacle is therefore circumvented, at the expense of appropriately transforming the original function f. This ploy is depicted in the following illustration :
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