Tutor profile: Robbie B.
Subject: Physics (Newtonian Mechanics)
A satellite orbits the earth. Explain why it is incorrect to refer to the force of gravity acting on the satellite as a centrifugal force.
Centrifugal force describes a force that pushes away from the center of the orbit. Centripetal force describes a force that pushes towards the center of the orbit. If gravity were instantaneously removed, the satellite would travel tangential to the orbit at the point where the gravity were removed. The satellite is not trying to flee the center of the orbit. The satellite would travel in a linear path except that gravity constantly pulls it towards the center of the orbit. Therefore, gravity should be referred to as a centripetal force and not a centrifugal force.
Subject: Mechanical Engineering
Explain St. Venant's principle and give an example of when this principle can be applied to simplify a problem.
St. Venant's principle states that the differences in the effect of two different, but statically equivalent (same magnitude and resolved point of application) decreases with distance from the point of application. At significantly large distances from the point of application, two statically equivalent loads have the same effect. When analyzing stresses in a structure or system, if the area of interest is far from the point of application of loads, a complex loading could be simplified for the purpose of the analysis. Suppose you wanted to analyze the stress in cantilever beam at the location where the beam is fixed. A triangular distributed load could be simplified as a point load by St. Venant's principle. If you were interested in the stresses at the center of the triangular distributed load, the simplification could not be made.
When should the product rule be used to find a derivative? Describe the product rule and apply it find the derivative of the following: (4x^2)(x-7)
The product rule is used when we need to take the derivative of the product of two functions. In the problem statement the function 4x^2 is multiplied with the function (x-7). Since the derivative of the product of these two functions is desired, we use the product rule. In words, the product rule goes "the derivative of the product of two functions is equal to the sum derivative of the first function times the second function and the derivative of the second function times the first". Summarized, if f(x)=g(x)*h(x), f'(x)=g'(x)*h(x)+h'(x)*g(x). The derivative of the function in the problem statement would be (8x)*(x-7) + (4x^2) or 12x^2 - 56x
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