RI 2023 Y5 Phy T3 CT Sect B Soln

Raffles Institution Year 5-6 Physics Department 1 2023 Year 5 H2 Physics Term 3 Common Test Solution Section B Important points to note 1. Quantitative questions (i.e. questions that involve calculations) • Write the concept used to solve (e.g. By the conservation of energy) and clearly state where it is being applied (e.g. from the bottom to the top of the circular motion). • Write the equation in words and/or in symbols. Use standard symbols (e.g. m for mass). Refer to the list of key quantities, their symbols and units in the syllabus document for the standard symbols used for the A-level examinations. If other symbols are used and it is not clear what quantity they represent, students would need to define them clearly. • Substitue all numerical values into the equation in the appropriate units. • Make the quantity to be determined the subject of the equation. • Write the answer to more than 3 significant figures. • Write the final answer to the appropriate number of significant figures and with units. 2. Qualitative questions (i.e. ‘explain’, ‘describe’ questions that involve writing in continuous prose) • Read the question carefully to be clear of the objective of the question. The number of marks allocated are a good indication of the demands of the question. • Write in full but short sentences. • Points presented should follow a logical sequence until the objective of the question is met. • State the specific Physics concepts/principles/definitions used to support the explanation. • Use specific Physics terminologies. • Equations may be used to support the explanation. However, equations must be accompanied with word explanations. • Do not use abbrievations especially for the important concepts used in the explanation (e.g. by COE, COM, POM). • Spell out all quantities (e.g. force instead of F , mass instead of m ). If there are too many quantities to define in a stated equation, then use standard symbols or the symbols that have already been defined in the question. However, for sybmols that could be ambiguous, students should spell these quantities out (e.g. if the explanation includes gravitational force and centripetal force, then using F G and FC is ambiguous if they are not defined). • S tudents should make use of the information/data given in the question to answer the question/deduce/draw conclusion as specificallly as possible (e.g. students should state that a quantity increases or decreases if the details given are sufficient to make this deduction, instead of just stating the quantity will not be the same or will change). • Read the answer again to ensure the objective of the question is met.

Raffles Institution Year 5-6 Physics Department 2 3. For ‘show’ questions, the marks allocated are for clear step-by-step working and explanations. No marks are given for the final answer since the answer is already given. Hence, all relevant working and substitutions have to be shown. If required to ‘show’ a numerical value, students are expected to calculate and write the answer to a larger number of significant figures than that required. This is then followed by writing the final answer to the correct number of significant figures required. (E.g. If the value to be shown is 3.45, students need to write 3.45112 first to show that they really did the calculations, before rounding off and writing the final answer as 3.45.) 4. For all quadratic equations, both solutions (positive and negative) have to be written down. Reject one of the solutions based on what the quantity is. (E.g. Reject negative answer for time.) 5. When dealing with equations involving vectors, always state the direction that is taken to be positive. 6. When applying the conservation of energy, state from which position to which position the conservation of energy is applied. Afterwhich, students are expected to write the conservation of energy as a word equation followed by the equation using symbols. The equations need to clearly show that all forms of initial energies is equal to all forms of final energies or equate the differences in all forms energies. All energy forms have to be included, even if that energy form is zero. Set that energy form to zero only when substituting in the numerical values to the equation. Accepted: • Applying conservation of energy from the bottom to the top of the circular motion, initial KE + initial GPE = final KE + final GPE 2211 22 iiffmv mgh mv mgh+= + OR decrease in KE = increase in GPE ( ) 2211 22 i f fimv mv mg h h−=− Not accepted: • Did not clearly show a difference in energies: 21 2 mv mgh= . • KE GPE∆= ∆ is equivalent to: final KE – initial KE = final GPE – initial GPE which is incorrect. Correct equation should be KE GPE−∆ =∆ . Note that ∆ means ‘change’ which is specifically used to mean ‘final – initial’. 7. Students should analyse and study these solutions well and learn/practise to present/craft their solutions/answers as given in these solutions. There is much room for improvement.

Raffles Institution Year 5-6 Physics Department 3 Solutions 1 (a) It introduces systematic error to the measurements. The diameter measurements will either be all smaller or all larger than the true value by a fixed amount which is the zero error that was unaccounted for. (b) (i) ( ) ( ) ( ) ( ) ( ) 2 2 23 2 77 2 4 1.50 0.23 10 4 0.32 40.0 10 4.8688 10 4.87 10 m LR A VdRA VA V d LL L L ρ π πρ π − − −− = = = = = × = × = ×=×Ω II I *The correct expressions to determine R and A should be shown clearly. (ii) 2 4 Vd L πρ = I ( ) 7 88 2 0.01 0.01 0.01 0.14.8688 10 2 1.50 0.23 0.32 40.0 6.201 10 6 10 m (1 s.f.) Vd L Vd L ρ ρ ρ − −− ∆∆ ∆∆∆= + ++ ∆= × + + +  = ×= ×Ω I I *Absolute uncertainty is always written to 1 s.f. (iii) ( ) ( ) 774.9 10 0.6 10 mρ −−=× ±× Ω *The d.p. have to be the same after expressing both to the same order of magnitude. (c) Accuracy is the degree of closeness between the mean value of the measurements, 74.9 10 m−×Ω , to the true value of 74.4 10 m−×Ω . OR Accuracy is whether the true value of 74.4 10 m−×Ω falls within 74.3 10 m−×Ω to 75.5 10 m−×Ω . Precision refers to the degree of agreement between repeated measurements of the same quantity which is represented by the uncertainty 70.6 10 mρ −∆= × Ω . OR Precision is the spread of the measurements which is represented by the uncertainty 70.6 10 mρ −∆= × Ω . *When distinguishing, reference to the definitions have to be made while bringing out the difference. *No conclusion on the accuracy and precision is required by the question. *Contradictions in the explanations are penalised.

Raffles Institution Year 5-6 Physics Department 4 2 (a) (i) 1. Taking direction downwards as positive, ( ) ( ) 2 2 2 1 2 1800 220sin15 (9.81) 2 1 (9.81) 220sin15 800 02 yy ys ut at tt tt = + = + + −=   ( ) ( ) ( ) ( ) 2 9.81 2 9.81 2 220sin15 220sin15 4 800 2 8.2238 or 19.832 (NA) 8.22 s t − °± ° − − = = − = 2. 1220cos15 212.504 m sxxvu −= = °= ( ) ( )( ) 22 2 1 2 220sin15 2 9.81 800 137.616 m s y y yy y v u as v − = + = °+ = ( ) ( ) ( )( ) ( ) ( )( ) 22 22 22 2 1 220cos15 220sin15 2 9.81 800 220 cos 15 sin 15 2 9.81 800 253.172 253 m s xyvvv − = + = °+ °+ = °+ ° + = = ( ) ( )( ) 2 11 220sin15 2 9.81 800 tan tan 32.9268 32.9220cos15 y x v vθ −− °+ = = = = °° magnitude = 1253 m s− direction = 32.9° clockwise below the horizontal OR (to determine speed) increase in K.E. = decrease in G.P.E. ( ) ( ) ( )( ) ( ) 22 221 11 22 2 2 9. 81 800 220 253.172 253 m s if if mv mu mg h h v gh h u − −=− = −+= + = = *Vague descriptions of the angle like ‘from horizontal’ or ‘to horizontal’ are not accepted unless it is accompanied by a diagram with angle correctly indicated. (ii) (220cos15 )(8.22) 1746.78 1750 m xxs ut= = ° = =

Raffles Institution Year 5-6 Physi