P2 Topic 4 - Motion and forces Higher

Transcription

1 Name: P2 Topic 4 - Motion and forces Higher Date: Time: Total marks available: Total marks achieved:

2 Questions Q1. A child is stationary on a swing. (a) The child is given a push by his brother to start him swinging. His brother applies a steady force of 84 N over a distance of 0.25 m. (i) Calculate the work done by this force. (2) (ii) State how much energy is transferred by this force. (iii) After several more pushes, the child has a kinetic energy of 71 J. The mass of the child is 27 kg. Show that the velocity of the child at this point is about 2.3 m/s. (iv) Which one of these quantities changes in both size and direction while he is swinging? Put a cross ( ) in the box next to your answer. A his gravitational potential energy B his momentum C the force of gravity acting on him D his kinetic energy *(b) The brother then stops pushing the child. The graph shows how the kinetic energy of the child varies over the next few swings. (2)

3 Explain the energy changes during this time. (6) (Total for Question is 12 marks) Q2. Momentum, energy and forces A box with a mass of 0.8 kg is lifted from the floor and placed on a shelf. The shelf is 1.8 m above the floor.

4 (a) (i) The box has gained gravitational potential energy. Calculate the gain in gravitational potential energy. Gravitational field strength = 10 N/kg (2) gain in gravitational potential energy =... J (ii) The box falls off the shelf. State the kinetic energy of the box just before it hits the floor.... J (iii) Just before the box hits the floor it has a momentum of 4.8 kg m/s. Calculate the velocity of the box just before it hits the floor. (3) velocity =... m/s *(b) The items in the box are packed in bubble wrap to protect them from damage. Explain, by considering changes either in momentum or in kinetic energy, how bubble wrap protects the items in a box from damage caused by a fall. (6)

5 Q3. A 60 kg student weighs 600 N. He does a bungee jump. The bungee cord becomes straight and starts to stretch when he has fallen 50 m. (a) Complete the sentence by putting a cross ( He first stops moving A before all the energy has disappeared B before the bungee cord starts to stretch C when the bungee cord is stretched the most D when the elastic potential energy is zero (b) Complete the sentence by putting a cross ( When his speed is 10 m/s his momentum is A 600 kg m/s B kg m/s C N m/s ) in the box next to your answer. ) in the box next to your answer. D N m/s (c) (i) Calculate the change in gravitational potential energy as the student falls 50 m. Give the unit. (3)

6 (ii) State at what point in the bungee jump the student has maximum kinetic energy. (iii) Explain why his maximum kinetic energy is likely to be less than your answer to (c)(i). (2) (Total for Question = 8 marks) Examiner's Report Q1. (a) (iii) In this type of "show that" question, candidates can score full marks in two ways. They can use the values supplied ( in this case 71J and 27 kg) and subsitute those into the equation given inside the fornt cover. They can then transpose this expression and perform any other required steps ( in this case finding a square root) to arrive at a result which can be compared with the "answer" ( in this case 2.3 m/s) An alternative and mathematically simpler method is to use the "answer" of 2.3 m/s and the given value of mass (27 kg) in the expression for kinetic energy. They can then evaluate this expression and compare the result with the KE given in the question. This requires no transposition and no calculation of a square root. This candidate has chosen to calculate the velocity from the KE and the mass. Results Plus: Examiner Comments Although v 2 is missing in the second line and 71 does not equal 0.5 x 27, the candidate's intentions are clear and the value of could only have been obtained by the correct mathematics. Full marks \

7 Results Plus: Examiner Tip Make sure that values on each side of an equals sign really are equal to each other. Here, the candidate has chosen the easier route. Results Plus: Examiner Comments A simple response which scores full marks. (b) This was the least well-answered question on the paper. It seemed that many candidates did not read the introduction carefully and gave answers which either implied or stated that the swings were decreasing in amplitude because the brother was still pushing but getting tired. Many other candidates tried to give explanations using the concepts of momentum, forces and acceleration rather than describing changes in kinetic energy. Another common misconception was that the kinetic energy was smallest when the swing was at the bottom. Examiners were looking for an explanation which described a continuous transfer between kinetic energy and gravitational potential energy. They were also looking for an understanding that this transfer was not perfect and that energy was being dissipated to the surroundings resulting in a gradual loss of kinetic energy. Rather than scoring individual marking points, examiners arrive at a judgement of the overall level of the response; taking into account how scientific terms are used to give a complete explanation. This is best shown by the examples below. A level 1 response would be a limited explanation which correctly stated some facts.

8 Results Plus: Examiner Comments This is a simple explanation which correctly states how kinetic energy changed over the cycle and where the kinetic energy was greatest. The use of language is suitable for this level. 2 marks A Level 2 response would be a simple explanation which linked facts together to explain one feature of the graph; either why the kinetic energy decreased and increased over one swing or why the maximum kinetic energy decreased over several swings. Results Plus: Examiner Comments This answer gives a clear description of the transfer between kinetic and gravitational potential energy. Although the candidate has mentioned the decrease in maximum kinetic energy, this has not been explained. Spelling, punctuation and grammar is suitable for this level. 4 marks.

9 Results Plus: Examiner Comments This response explains why the maximum kinetic energy decreases over several cycles and is at level 2. It does not mention the transfer between kinetic energy and gravitational potential energy. It scored 4 marks. Level 3 responses gave a full explanation of both features of the graph.

10 Results Plus: Examiner Comments A well written response which explains both the transfer between kinetic energy and gravitational potential energy and the gradual decrease in maximum kinetic energy. All scientific terms are used correctly. Full marks at level 3. Candidates need to be especially careful with their English as well as their Physics.

11 Results Plus: Examiner Comments Although the scientific explanation is correct and is at level 3, the answer has many errors of spelling, punctuation and grammar. 5 out of 6 marks only. Results Plus: Examiner Tip Make sure that you use capital letters and punctuation correctly. If you do not then you will lose marks in this type of question.

12 Q2. No Examiner's Report available for this question Q3. (c) (i) There were three explicit calculations on this paper - 2ci, 3aiii and 5aii. All were good discriminators near the C/D boundary. Near the A boundary nearly all scored full marks. Results Plus: Examiner Comments This candidate received full marks (2) for the numerical calculation plus 1 mark for the unit. Total score: 3 marks. Results Plus: Examiner Comments Without the unit, this answer is worth 2 marks.

13 Results Plus: Examiner Comments Although some 'working' is shown, the absence of a written equation cannot help to score any marks for substitution - score 0. Results Plus: Examiner Tip Copy the equation you intend to use from the data sheet provided. In this case however, the incorrect use of 600 instead of 10 for g would have prevented you scoring. Results Plus: Examiner Comments When asked for, the unit mark can be scored independently of the numerical working. This response was therefore worth 1 mark.

14 Results Plus: Examiner Tip Think what you are calculating and recall the unit for that quantity - ie distance - m, force - N, power - W etc. (c) (ii) This item followed a multiple choice item (2a) in which two of the options covered large periods of time (before...) and the key and one other showed instants of time (when...). The multiple choice item produced good discrimation by reflecting performance on the paper as a whole. Results Plus: Examiner Comments This response expressed the point needed concisely and scored the mark. Other correct responses included 'after falling 50 m' and 'just as the cord becomes straight'. The stem describes how the cord 'becomes straight and starts to stretch when he has fallen 50 m.' One common misconception involved mixing up KE and GPE. Results Plus: Examiner Comments This is an exact single moment in time but was incorrect and scored 0. Other responses were vague such as 'while falling', 'when stretching' or 'at the bottom' (of what). (c) (iii) The inefficiency of energy transfers was tested here. Many candidates presented either the energy transfer or the reason for this. Few presented both.

15 Results Plus: Examiner Comments The idea that the surroundings are heated scored 1 mark and 'due to air resistance' scored the second. Marks are often lost through the use of the general words 'it', 'they' etc. Results Plus: Examiner Comments The 'it' here could refer to some energy, heat energy etc. Results Plus: Examiner Tip When writing, try to avoid using words such as 'it' and 'they'. Take the little extra time needed to say exactly what you mean. A variety of incorrect numerical responses were given for this. The most common referred to the fact that calculations of KE involve the factor of 1/2 and 'so must be less than the other'. Another example involved the gravitational field strength.

16 Results Plus: Examiner Comments This scored 0. Mark Scheme Q1. (a)(i) Answer substitution work done = evaluation 21(J) Acceptable answers Full marks for correct answer even if no working is evident Mark (a)(ii) 21 J Ecf from (a)(i) (a)(iii) substitution KE = ½ 27 x (2.3) 2 evaluation = 71.4 (which is approx 71) V=2.29 gains two marks Reverse argument which shows that V = 5.3 gains two marks (2) (a)(iv) B (2) *(b) Indicative Content An explanation linking some of the following points kinetic energy varies during swing kinetic energy maximum at bottom of swing kinetic energy minimum at top of swing gravitational potential energy(gpe) varies Mark (6)

17 during swing gpe maximum at top of swing gpe minimum at bottom of swing (continuous) interchange of KE and gpe total amount of energy is constant during one swing over a number of swings max KE and max PE decreases energy is dissipated/'lost' to surroundings because of air resistance / friction amplitude/size of swings decrease ( as energy 'lost' to surroundings) ignore references to momentum Level Mark Descriptor 0 No rewardable content a limited explanation which states some facts e.g. (max) Kinetic energy decreases over time. KE will transfer to GPE. or KE increases and decreases over one swing. The height which the swing reaches gets less over time. the answer communicates ideas using simple language and uses limited scientific terminology spelling, punctuation and grammar are used with limited accuracy a simple explanation with links between facts; either over one period of oscillation or over several periods of oscillations. Kinetic energy decreases as he gets higher and the GPE increases. There is a continuous interchange of KE and gpe as he swings. or KE is gradually transferred to heat so swing rises to a slightly lower height each time. the answer communicates ideas showing some evidence of clarity and organisation and uses scientific terminology appropriately spelling, punctuation and grammar are used with some accuracy a detailed explanation with links between

18 facts over one period of oscillation and over several periods of oscillations e.g. kinetic energy is at a maximum at bottom of swing There is a continuous interchange of KE and gpe. KE (and gpe) reduce over a number of swings as energy is dissipated to the surroundings due to friction. the answer communicates ideas clearly and coherently uses a range of scientific terminology accurately spelling, punctuation and grammar are used with few errors Q2. Question Answer Acceptable answers Mark Number (a)(i) substitution evaluation 14.4 (J) give full marks for correct answer, no working (2) Question Answer Acceptable answers Mark Number (a)(ii) 14.4 (J) e.c.f from part (i) Question Answer Acceptable answers Mark Number (a)(iii) substitution 4.8 = 0.8 v transposition v = 4.8/0.8 evaluation 6 (m/s) allow substitution and transposition in either order give full marks for correct answer, no working (3) Question Indicative Content Mark Number QWC *(b) An explanation linking some of the following points Either momentum item must lose momentum in order to come to rest force of impact depends on rate of change of momentum if item is dropped from greater height then velocity at impact is greater so momentum to be lost is greater bubble wrap works by increasing the time taken for the item to come to rest reduces the rate of change of momentum this (6)

19 reduces the force of impact to a safe value Or kinetic energy item must lose kinetic energy in order to come to rest force of impact depends on work done if item is dropped from greater height then velocity at impact is greater so kinetic energy to be lost is greater loss of kinetic energy equals work done bringing item to rest bubble wrap works by increasing the distance travelled for the item to come to rest this reduces the force of impact to a safe value Level 0 No rewardable content a limited explanation of the cushioning effect e.g. bubble wrap reduces the force of impact the answer communicates ideas using simple language and uses limited scientific terminology spelling, punctuation and grammar are used with limited accuracy some explanation linking cushioning effect with either increased time of impact or increased distance of impact e.g. bubble wrap reduces the force of impact by increasing the time of impact the answer communicates ideas showing some evidence of clarity and organisation and uses scientific terminology appropriately spelling, punctuation and grammar are used with some accuracy a detailed explanation linking either force with rate of change in momentum or energy with work done and distance e.g. the bubble wrap increases the time of impact which reduces the rate of change of momentum which reduces the force of impact the answer communicates ideas clearly and coherently uses a range of scientific terminology accurately spelling, punctuation and grammar are used with few errors

20 Q3. Answer Acceptable answers C when the (a) bungee cord is stretched the most (b) A 600 kg m/s (c)(i) Substitution: give two marks for or 600 correct answer no 50 Evaluation: working j / joule Unit: 30 kj for full marks J / Nm (3) (c)(ii) (c)(iii) After falling 50 m / when the cord becomes straight/when cord starts to stretch An explanation linking any two of not all GPE is transferred to KE some of the GPE transfers to thermal energy /work is done due to drag Mark tension starting to increase at terminal velocity ignore maximum velocity/speed not all GPE goes to KE maximum energy is same (value) as GPE before falling /speed does not reach the speed at which he should fall some lost as heat/sound (of rope or movement through air) (air) resistance / friction ignore wind (2)