Last time we introduced a physics concept known as torque and how it, together with modified gear ratios, can produce a mechanical advantage in devices whose motors utilize gear trains. Now we’ll familiarize ourselves with torque’s mathematical formula, which involves some terminology, symbols, and concepts which you may not be familiar with, among them, vectors, and sin(ϴ). Torque = Distance × Force × sin(ϴ) In this formula, Distance and Force are both vectors. Generally speaking, a vector is a quantity that has both a magnitude — that is, any measured quantity associated with a vector, whether that be measured in pounds or inches or any other unit of measurement — and a direction. Vectors are typically represented graphically in engineering and physics illustrations by pointing arrows. The arrows are indicative of the directionality of the magnitudes involved. Sin(ϴ), pronounced sine thaytah, is a function found within a field of mathematics known as trigonometry , which concerns itself with the lengths and angles of triangles. ϴ, or thaytah, is a Greek symbol used to represent the angle present between the Force and Distance vectors as they interact to create torque. The value of sin(ϴ) depends upon the number of degrees in the angle ϴ. Sin(ϴ) can be found by measuring the angle ϴ, entering its value into a scientific calculator, and pressing the Sin button. We’ll dive into the math behind the vectors next time, when we return to our wrench and nut example and apply vector force quantities.
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Posts Tagged ‘engineering’
Vectors, Sin(ϴ), and the Torque Formula
Wednesday, March 26th, 2014Tech Quiz Number 1
Thursday, August 13th, 2009A Few Words About Electric Shocks
Sunday, July 26th, 2009 For an electric shock to occur, a person must become a part of an electrical circuit in such a way that electric current passes over their skin or through their body. Under certain conditions, even momentary contact with an energized metal object can result in serious injury and even death. According to an article in the American Journal of Industrial Medicine:
From an engineering viewpoint, the body’s electrical resistance is an important variable. Electrical resistance of an object is a measure of how freely electrical current can flow across the object when a voltage is applied across it. Resistance is measured in units called “Ohms.” Resistance of a person’s body can depend on skin dryness, perspiration level, thickness of the skin, the distance that the electrical current travels through the skin, and other factors. The typical human body has a handtohand electrical resistance somewhere between 1,000 and 2,000 Ohms, but resistance across other parts of the body can be much higher. There is a wide variation in body resistance between individuals, so the same voltage level may result in different effects. Most electrical injuries occur from alternating current (AC) at levels above 50 Volts at the low frequencies typically maintained by electric utilities. The North American utilities normally generate power at a frequency of 60 cycles per second. The “cycles per second” unit of frequency is also referred to as “Hertz,” usually abbreviated as “Hz.” At 60Hz frequency, the threshold for perception occurs with electrical currents as low as 0.0001 Amps. The “can’t let go” electrical current for adults is approximately 0.010 to 0.015 Amps. This is the current that causes involuntary muscle contractions severe enough to prevent the person from letting go of the source of the electrical shock. Electric currents as low as 0.050 Amps at 120V, 60Hz, have been known to cause death. Just to give you an idea of how small that current is… a table lamp with one 40 Watt incandescent bulb draws 0.333 Amps from a 120 Volt, 60 Hz household electrical outlet! In the interest of electrical safety, the National Electrical Code (NEC) considers 0.005 Amps at 120V, 60Hz to be the safe upper limit for children and adults. ____________________________________________________________________
