Life is like riding a bicycle.  To keep your balance you must keep moving.”
Albert Einstein

Sunday, April 24, 2011

AP Physics Exam – Be Careful While Answering Free Response Questions

“The best thinking has been done in solitude. The worst has been done in turmoil.”

– Thomas A. Edison

While answering multiple choice questions in all entrance tests you enjoy freedom to a great extent. The examiner who evaluates your performance does not bother how you arrived at the answer. You arrive at the correct option using your own ways, making mental manipulations and jotting things in the space provided for rough work on your answer sheet. The examiner does not (and need not) care to see what you have written in that space. You can use short-cuts to the maximum extent to arrive at the answers in the minimum time so that you can attempt all questions. But answering free response questions is different altogrther.

While answering AP Physics free response questions you have to be very careful to avoid likely chances of losing points. You are expected to show your work clearly in the spaces provided for the solution of the free response questions. The basic point you must remember is that the examiner who evaluates your answer script finds chances for awarding you points. If you do not know the full solution of a question but know partial solution, never hesitate to supply whatever you know relevant to that question. Understand that some thing is better than nothing. Partial solution will bring you partial credit. But in such cases also show all your work so as to give the Exam Reader a chance to give you points for what you have presented.

I’ll show you a simple instance of a likely lapse on your part while answering free response questions. Consider the following which is only a part of a bigger question:

Tom weighing 60 kg and Jack weighing 80 kg are ice skaters at rest on smooth horizontal terrain and are facing each other. They push each other for 0.5 second, which makes them glide apart. Tom’s speed immediately after separating from Jack is 1 ms–1.

Neglecting friction during the push, calculate the speed of Jack immediately after separating from Tom.

You know that you can work this out immediately by applying the law of conservation of momentum. Since the total initial momentum of the system (consisting of Tom and Jack) is zero and there are no external forces [the forces exerted by Tom and Jack are internal forces within the system], the total final momentum (immediately after the separation) also must be zero. You mentally figure out that the momentum of Tom is equal and opposite to that of Jack and hence the magnitude of Tom’s momentum is the same as that of Jack. Tom’s momentum is 60×1 = 60 kg ms–1 and hence Jack’s speed immediately after separating from Tom is 60/80 = 0.75 ms–1.

Suppose in a hurry you write the answer as given below:

Jack’s speed immediately after separating from Tom = 60/80 = 0.75

If the above part of the question carries 2 points you are likely to get 1 point only since you have kept the Exam Reader at dark as to how you arrived at the answer and you have not expressed the unit of speed (ms–1). All final numerical answers should include proper units.

You need not waste your time with lengthy reasoning in support of your answer. But you should supply some brief verbal or mathematical reasoning. In the case of the above question you are expected to write something like this:

From the law of conservation of momentum, the total final momentum is zero since the total intial momentum is zero. The momentum of Tom immediately after separation is equal and opposite to that of Jack so that the magnitudes of their momenta are equal.

Or, m1v1 = m2v2 where m1 is mass of Tom, v1 is his speed, m2 is mass of Jack and v2 is his speed.

Therefore v2 = m1v1/m2 = (60×1)/80 = 0.75 ms–1.

As you should definitely know, the words “what is”, “determine”, “calculate” and “derive” used in the AP Physics free response questions have distinct meanings. The words “what is” and “determine” usually imply that the work leading to a final answer need not be explicitly shown to obtain the full credit eventhough it will be a good idea to include it briefly to impress the Exam Reader and to gain partial points even if your final answer is incorrect.

In the partial question we considered above you were required to ‘calculate’ Jack’s speed immediately after getting separated from Tom. The word “calculate” implies that you are required to show your steps leading to the final answer. The word “derive” indicates that you have to begin your derivation with fundamental equations of the type given in the AP Physics Exam equation sheets.

Often parts of questions beginning with “what is” will be followed by a line such as “justify” your answer. Do not skip that justification part in a hurry. It will carry significant points and so you must supply verbal or mathematical justification in support of your answer.

The College Board gives important details to help you in your endeavour. Visit the site and clear all your doubts.

The AP Physics Exam is fast approaching and you may be experiencing the inevitable exam stress. Here is a piece of advice to you

Tuesday, April 12, 2011

AP Physics C – Additional Practice Questions (MCQ) on Electromagnetic Induction

"There's a way to do it better - find it"
Thomas A. Edison

In my last post I had given you a few multiple choice practice questions (with solution)
involving electromagnetic induction. Today we will discuss a few more questions in this section. These are meant for AP Physics C aspirants even though AP Physics B aspirants also will find them useful:

(1) The adjoining figure shows a 1000 turn coil of fine insulated copper wire connected to the y-inputs A and B of a cathode ray oscilloscope set for displaying the voltage wave form induced in the coil. A bar magnet, with its axis vertical and coinciding with the axis of the coil, is initially at rest, with its centre O at a height 10 cm from the centre of the coil. The bar magnet is allowed to fall freely under gravity and the induced voltage as a function of time is displayed on the screen of the oscilloscope. Which one among the following graphs best represents the induced voltage?

The magnetic flux linked with the coil increases up to the instant when the centres of the magnet and the coil coincide. Thereafter the magnetic flux decreases. Therefore, the direction of the induced emf gets reversed. The reversal of the induced emf occurs at the instant when the centres of the magnet and the coil coincide since the rate of change of magnetic flux at that instant is zero even though the flux linkage is maximum. Further, the latter half of the induced voltage has a peak of greater magnitude since the speed of fall of the magnet is greater so that the rate of change of magnetic flux is greater. The correct option is (a).

(2) The voltage variation across a resistance R in a series LR circuit is displayed as a function of time using a cathode ray oscilloscope. The swith S is closed at time t = 0 and then opened at time t = t1. Which one among the following graphs best represents the voltage variation across R during the time interval 0 to t1?

When the switch S is closed,the time constant of the circuit is L/R and is significant. The current I in the circuit therefore does not rise abruptly to the final maximum value I0 (let us say). . The rise of current is exponential and hence the voltage across the resistance R rises exponentially with time.

[The exponential growh of the current I is given by I = I0(1 – eRt/L) where e is the base of natural logarithms].

When the switch S is opened at the instant t1 the open circuit at the switch makes the resistance of the circuit infinite and hence the time constant becomes zero. The current drops abruptly to zero. The voltage drop across R also drops abruptly to zero. The correct option is (e).

[The graph (d) may distract you. The growth of the voltage shown in it is not exponential. In an exponential growth, the initial rate of growth will be the largest].

(3) The switch S in the circuit shown is closed and sufficient time is allowed so that the current through the inductance L and the resistance R becomes the final steady value. The inductance L is about 20 henry and the resistance R is about 10 ohm. The switch S is opened at time t = 0. Then the voltmeters V1 and V2 will indicate the same reading at

(a) time t = 0

(b) time t = L/R

(c) rime t = 2 L/R

(d) time t = L/2R

(e) all times

This question is very simple but it may confuse you.

Since the LR circuit has a non-zero time constant (L/R), the voltmeter readings will not become zero abruptly but will drop to zero exponentially with time. Since the inductance and resistance are connected in parallel, the voltmeters V1 and V2 will indicate the same reading at all times [Option (e)].