Cambridge A Level Physics 9702 — 2019 May/June Paper 5 · Variant 1

1 A student is investigating the bending of a loaded wooden strip. Fig. 1.1 shows a rectangular strip of width b and thickness t overhanging the edge of a bench. A length L of the strip is unsupported. strip b P t L bench Fig. 1.1 A load of mass M is positioned at point P. This causes the unsupported part of the strip to bend with a deflection s, as shown in Fig. 1.2. bench s Fig. 1.2 (not to scale) It is suggested that the relationship between s and L is 4MgL3 E = bst 3 where g is the acceleration of free fall and E is the Young modulus of the wood. Design a laboratory experiment to test the relationship between s and L. Explain how your results could be used to determine a value for E. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to: • the procedure to be followed • the measurements to be taken • the control of variables • the analysis of the data • any safety precautions to be taken. 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Mark scheme: 1 Defining the problem L is the independent variable and s is the dependent variable or vary L and measure s 1 keep mass of load or M constant 1 Methods of data collection labelled diagram of workable experiment including: • method of fixing strip at one end, e.g. with a G-clamp or (heavy) mass placed on top of strip over bench • load shown touching at point P • load and G-clamp or (heavy) mass labelled 1 method of attaching load to strip, e.g. use glue/tape/attach with a hook and string 1 use a rule to measure L and s 1 use a balance to measure M 1 Method of analysis plot a graph of s against L3 (allow lg s against lg L, or log) 1 relationship valid if a straight line through (0,0) (for lg s against lg L gradient of straight line = 3) 1 3 4 gradient Mg E bt = × (for lg s against lg L, − = ÷ intercept 3 4 10y Mg E bt ) 1 Question Answer Marks 1 Additional detail including safety considerations Max. 6 D1 use cushion/foam/sandbox in case mass/load falls or wear goggles in case strip snaps or recoils D2 use same wooden strip or keep b and t constant D3 clamp rule vertically to measure s D4 method to ensure clamped rule to measure s is vertical, e.g. correctly positioned set square indicated at right angles to the horizontal surface or plumb line shown in appropriate position D5 s = reading of vertical rule with loaded strip – reading of vertical rule with no load D6 repeat s measurement for each L (unloading and loading strip) and average s D7 use a micrometer/calipers to determine t D8 repeat readings for b and/or t at different points along/across the strip and average D9 method to ensure strip is perpendicular to the bench, e.g. repeat measurements of L on each side of strip to check that L is constant or set square correctly indicated on diagram D10 wait until block is stationary/in equilibrium or measure s after a fixed time

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2 A student is investigating a rotary variable resistor, as shown in Fig. 2.1. spindle variable resistor Fig. 2.1 The variable resistor is connected to a battery of electromotive force (e.m.f.) E and negligible internal resistance, as shown in Fig. 2.2. E A Fig. 2.2 The student uses a protractor to measure the angle θ through which the spindle of the variable resistor is rotated and records the current I. The experiment is repeated for different angles. It is suggested that I and θ are related by the equation E = IKθ where K is a constant. 1 on the y-axis against θ on the x-axis. (a) A graph is plotted of I Determine an expression for the gradient. gradient = ......................................................... [1] (b) Values of θ and I are given in Fig. 2.3. 1 θ/ ° I / mA / A–1 I 95 5.7 ± 0.1 115 4.7 ± 0.1 135 4.0 ± 0.1 155 3.5 ± 0.1 175 3.1 ± 0.1 195 2.7 ± 0.1 Fig. 2.3 1 Calculate and record values of / A–1 in Fig. 2.3. I 1 Include the absolute uncertainties in . [2] I 1(c) (i) Plot a graph of / A–1 against θ/ °. I 1 Include error bars for / A–1. [2] I (ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2] (iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer. gradient = ......................................................... [2]

Mark scheme: 2(a) gradient = K E 2(b) 1 I / A–1 180 or 175 210 or 213 250 290 or 286 320 or 323 370 1 uncertainties in 1 I from ±3 or ±4 to ±10–15 1 2(c)(i) Six points plotted correctly. Must be accurate to the nearest half small square. Diameter of points must be less than half a small square. 1 Error bars in 1 I plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical. 1 Question Answer Marks 2(c)(ii) Line of best fit drawn. Do not allow line from top point to bottom point. If points are plotted correctly then lower end of line should pass between (122, 230) and (126, 230) and upper end of line should pass between (186, 350) and (190, 350). 1 Worst acceptable line drawn (steepest or shallowest possible line that passes through all the error bars). All error bars must be plotted. 1 2(c)(iii) Gradient determined with clear substitution of points from the line into ∆y/∆x. Distance between points must be at least half the length of the drawn line. 1 uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient) 1 2(d) 9.4 ± 0.2 (V) 1 2(e)(i) K determined from gradient and given to 2 or 3 significant figures. K = E × gradient = 9.4 × (c)(iii). 1 K determined from gradient with correct unit (Ω / °). 1 2(e)(ii) gradient % uncertainty in 100 gradient E K E     ∆ ∆   = + ×             1 Question Answer Marks 2(f) θ calculated. Correct substitution of numbers required. 9.4 0.01 E K θ = = × (e)(i) I or 1 1 gradient 0.01 θ = = × ×(c)(iii) I 1 Absolute uncertainty in θ. Correct substitution of numbers required. Use of ∆I not required but allow if included by the candidate. Using E and K: θ θ   ∆ ∆ ∆   = + + ×         uncertainty in E K E K I I 0.2 uncertainty in 9.4 100 θ θ   = + ×     (e)(ii) max min max min 0.01 min 0.01 max E E K K θ θ = = × × or Using gradient: θ θ   ∆ ∆   = + ×         gradient uncertainty in gradient I I 1 1 max min 0.01 mingradient 0.01 maxgradient θ θ = = × × or 1

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