Tuesday, December 10, 2013

Positive Sides of Knowing about Negative Signs

As the old adage goes, “Looks can be deceptive,” the same at times holds good in the realm of physics. What appears to be insignificant can have astronomical bearing on the results of some problems. In this post we will be focusing on one such thing, i.e. the negative signs. Many a times, I have seen my students getting perplexed when they encounter a negative sign as a result at the end of some tedious mathematical calculations lurking in some physics problems. They get frustrated assuming that all their effort went in vain when the result is negative. I have just one word for it. Relax! There is no need to panic. There can be various implications that can be derived from a negative result bearing the negative sign. So, get ready for some GYAAN on how you can interpret results with negative signs after doing your calculation. In Physics, Mathematics often generates answers that you might not have thought of as possibilities. If you get more answers than you expect, do not automatically discard the ones that do not seem to fit. Examine them carefully for physical meaning. For example, if the time is your variable, even a negative value can mean something; negative time simply refers to time before t=0, the (arbitrary) time at which you decided to start your stopwatch. Here is another misconception; in common language, the sign of acceleration has a nonscientific meaning: positive acceleration means that the speed of an object is increasing, and the negative acceleration means that the speed is decreasing (the object is decelerating). However in many problems of Kinematics, the sign of acceleration indicates a direction, not whether an object’s speed is increasing or decreasing. For example, if a car with an initial velocity v= -25 m/s is braked to a stop in 5 s, then a(avg) = +5 m/s^2. The acceleration is positive, but the car’s speed has decreased. The reason is the difference in signs: the direction of the acceleration is opposite that of the velocity.
Also, for falling-body problems, we establish a vertical axis (the y axis) and we choose – quite arbitrarily- its upward direction to be positive. We then choose the origin of the y axis (i.e. the y=0 position) to suit the problem. A negative value of y then means that the body is moving in the negative direction of the y axis – i.e. downward. This is true no matter where the body is located. We take the acceleration to be negative (-9.8 m/s^2) in all problems dealing with falling bodies. A negative acceleration here means that, as time goes on, the velocity of the body becomes either less positive or more negative. This is true no matter where the body is located and no matter how fast or in what direction it is moving. Hence, here is the proper way to interpret the signs: If the signs of the velocity and acceleration of a particle are the same, the speed of the particle increases. If the signs are opposite, the speed decreases. Keep visiting TCYonline.com for more Tips and tricks on NTSE, NSEJS & Olympiads. Remember, we here at TCY are committed to your success.

No comments:

Post a Comment