A-LevelPhysicsForces, density and pressure9702/33 · Feb/Mar 2017 · Q120 Marks

In this experiment, you will investigate forces on a wooden strip in equilibrium.

(a)(i)Assemble the apparatus as shown in Fig. 1.1, with the mass resting on the bench.
(a)(ii)Adjust the height of the boss and the position of the mass until the wooden strip is parallel to the bench and the springs are vertical.
(a)(iii)Measure and record the lengths l₁ and l₂ of the coiled sections of the two springs, as shown in Fig. 1.1. l₁ = l₂ = [1][1]
(b)(i)Hang the hook and about half the rings from string loop Y.
(b)(ii)Repeat (a)(ii) and (a)(iii). l₁ = l₂ =
(b)(iii)Using the data from the card, calculate the total mass m hanging from string loop Y. m = [1][1]
(c)Change m by altering the number of rings on the hook, and repeat (a)(ii), (a)(iii) and (b)(iii) until you have six sets of values of m, l₁ and l₂. Record your results in a table. Include values of (l₂ – l₁) in your table. [8][8]
(d)(i)Plot a graph of (l₂ – l₁) on the y-axis against m on the x-axis. [3][3]
(d)(ii)Draw the straight line of best fit. [1][1]
(d)(iii)Determine the gradient and y-intercept of this line. gradient = y-intercept = [2][2]
(e)It is suggested that the quantities l₁, l₂ and m are related by the equation (l₂ − l₁) = am + b where a and b are constants. Use your answers from (d)(iii) to determine the values of a and b. Give appropriate units. a = b = [2][2]
(f)The spring constant k of each spring can be found using the relationship k = g/a where g = 9.81 Nkg⁻¹. Calculate k. k = [2][2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

[1] Values of l1 and l2, both with units, and l2 > l1
[1] Value of m in range 30 to 70 g, with unit.
[5] Six sets of readings of l 1, l 2 and m with correct trend and without help scores 5 marks, five sets scores 4 marks etc.
[1] Range: mmax ≥ 80.0 g and mmin < 30.0 g.
[1] Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. (l2-l1)/mm.
[1] Consistency: All values of l4 and l2 must be given to the nearest mm.
[1] Axes: Sensible scales must be used, no awkward scales (e.g. 3:10). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity which is being plotted. Scale markings should be no more than 3 large squares apart.
[1] Plotting of points: All observations must be plotted on the grid. Diameter of plotted points must be < half a small square (no blobs). Plots must be accurate to within half a small square in both x and y directions.
[1] Quality: All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be no more than ±10.0 g in the m direction from a straight line.
[1] Line of best fit: Judged by balance of all points on the grid (at least 5) about the candidate's line. There must be an even distribution of points either side of the line along the full length. One anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate. Lines must not be kinked or thicker than half a small square.
[1] Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct. Both read-offs must be accurate to half a small square in both the x and y directions.
[1] y-intercept: Either Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with read-off accurate to half a small square in both x and y directions. Or Intercept read directly from the graph, with read-off at x = zero accurate to half a small square in y direction.
[1] Value of a equal to candidate's gradient. Value of b equal to candidate's intercept. The values must not be fractions and must be to at least 2 sig. fig.
[1] Unit for a is dimensionally correct. Unit for b is dimensionally correct.
[1] k calculated correctly.
[1] k given to 2 or 3 s.f.