Exam Tips: Comparison between two quantities
Comparison question is a popular type of question. It often requires good mathematically skills and clear presentation of the steps of solution. You might be able to work out the answer very quickly in your mind, base on logical sense and strong foundation of mathematics. However, a clear and organised presentation is very important for you to get optimum marks if your final answer is incorrect due to wrong calculation. In this post, I suggest a structured problem solving technique that you can learn to apply if you have not had one. Once you have got used to the method, you will be able to simplify the steps into just a few lines.
Example question: 9702/22/M/J/2016 Question 3(b)
The Young modulus of steel is 1.9 × 1011 Pa. The Young modulus of copper is 1.2 × 1011 Pa.
A steel wire and a copper wire each have the same cross-sectional area and length. The two wires are each extended by equal forces.
(i) Use the definition of the Young modulus to determine the ratio
extension of the copper wire / extension of the steel wire
Steps of solution:
1. Identify the equation: Y.M. = [ force x original length ] / [ area x extension ]
E = F x L / A x e
2. Tabulate the quantities into a table:
3. Move all constants to one side:
So, Eses;= Ecec
4. Now you can rearrange to the ratio required, ie
extension of the copper wire / extension of the steel wire
Eses = Ecec
Es/ Ec = ec/es
ec/es = 1.9 × 1011/ 1.2 × 1011
= 1.58 (do not leave in fraction)
Now, let's try another question:
Example question: 9702/11/M/J/2016 Q27
Fringes of separation x are observed on a screen 1.00 m from a double slit that is illuminated by
yellow light of wavelength 600 nm.
At which distance from the slits would fringes of the same separation x be observed when using
blue light of wavelength 400 nm?
Steps of solution:
1. Equation: x = λD / a
2. Tabulate the quantities into a table:
Example question: 9702/22/M/J/2016 Question 3(b)
The Young modulus of steel is 1.9 × 1011 Pa. The Young modulus of copper is 1.2 × 1011 Pa.
A steel wire and a copper wire each have the same cross-sectional area and length. The two wires are each extended by equal forces.
(i) Use the definition of the Young modulus to determine the ratio
extension of the copper wire / extension of the steel wire
Steps of solution:
1. Identify the equation: Y.M. = [ force x original length ] / [ area x extension ]
E = F x L / A x e
2. Tabulate the quantities into a table:
| steel | copper |
|---|---|
| Es | Ec |
| A | A |
| L | L |
| F | F |
| es | ec |
3. Move all constants to one side:
E = FL / Ae
Ee = FL/A = constant
So, Eses;= Ecec
4. Now you can rearrange to the ratio required, ie
extension of the copper wire / extension of the steel wire
Eses = Ecec
Es/ Ec = ec/es
ec/es = 1.9 × 1011/ 1.2 × 1011
= 1.58 (do not leave in fraction)
Now, let's try another question:
Example question: 9702/11/M/J/2016 Q27
Fringes of separation x are observed on a screen 1.00 m from a double slit that is illuminated by
yellow light of wavelength 600 nm.
At which distance from the slits would fringes of the same separation x be observed when using
blue light of wavelength 400 nm?
Steps of solution:
1. Equation: x = λD / a
2. Tabulate the quantities into a table:
| 1 | 2 |
|---|---|
| x | x |
| D1 | D2 |
| λ1 | λ2 |
| a | a |
3. Move all constants to one side:
λD = xa = constant
λ1D1 = λ2D2
(600)(1.00) = (400)(D2)
D2 = 1.50 m
Hey can you do 9702 11 mj 2016 q27 Complete question i can't figure out the graphs
ReplyDeleteHi Fatima, why do you need a graph for this question?
ReplyDeleteDo you mean q27 on Paper 13?
No. In this question part b ii they have asked a graph question i need that one
DeleteHi Fatima, I think you are asking about 9702/22/M/J/2016 Question 3(b)(ii), right? Ratio of ec/es is 1.58 means under the same force, copper extension is 1.58 times of steel extension, means that graph of copper is less steep compared to steel. PM me if you are still confused.
Delete03262148269
ReplyDelete