A student investigates the collision of two gliders A and B on a linear air-track. A card is attached to glider B, as shown in Fig. 2.1. [Figure 2.1] Glider B has a mass M. A mass m is added to glider B. Glider A travels at a constant velocity u towards the stationary glider B. The gliders then collide and move together towards the light gate. The card passes through the light gate which is connected to a data logger. The student records the velocity v of the two gliders from the data logger. The student changes the mass m and repeats the experiment. It is suggested that v and m are related by the equation Au = (M + m + A)v where A is the mass of glider A.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [1] gradient = 1/uA
2. [1] y-intercept = 1/u
3. [1] Values of (M + m) and 1/v as shown above: (M+m)/g: 380, 480, 580, 680, 830, 930 1/v /scm⁻¹: 0.226 or 0.2262, 0.255 or 0.2551, 0.294 or 0.2941, 0.331 or 0.3311, 0.388 or 0.3876, 0.429 or 0.4292
4. [1] Absolute uncertainties in (M + m) from ± (19 or 20) to ± (46.5 or 47 or 50).
5. [1] Six points plotted correctly. Must be accurate to the nearest half a small square. Diameter of points must be less than half a small square.
6. [1] Error bars in (M + m) plotted correctly. All error bars must be plotted. Total length of bar must be accurate to less than half a small square and symmetrical.
7. [1] Line of best fit drawn covers all points. Points must be balanced. Do not allow line from top point to bottom point. Line must pass between (425, 0.240) and (440, 0.240) and between (850, 0.400) and (865, 0.400).
8. [1] Worst acceptable line drawn (steepest or shallowest possible line that passes through all error bars). All error bars must be plotted.
9. [1] Gradient determined with clear substitution of data points into Δy / Δx. Distance between data points must be at least half the length of the drawn line.
10. [1] Gradient of worst acceptable line determined.
11. uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
12. [1] y-intercept determined by substitution of correct point into y = mx + c.
13. [1] y-intercept of worst acceptable line determined by substitution into y = mx + c.
14. uncertainty = (y-intercept of line of best fit – y-intercept of worst acceptable line) or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept)
15. [1] u determined using y-intercept and u and A given to two or three significant figures. u = 1 / y-intercept
16. [1] A determined using gradient with correct substitution and units with correct power of ten for u and A. A = y-intercept / gradient or A = 1 / (u × gradient)
17. [1] Percentage uncertainty in A determined, e.g. percentage uncertainty in A = (Δgradient / gradient + Δy-intercept / y-intercept) or Δu clearly determined using the value of u and percentage uncertainty in A = (Δgradient / gradient + Δu / u) × 100 or correct substitution for max/min methods e.g. max A = 1 / (min u × min gradient) min A = 1 / (max u × max gradient)
18. [1] Value of m determined from (d)(i) or (c)(iii) and (c)(iv), with correct number substitution and correct power of ten. m = (A × u) / v - (M + A) or m = (0.5 - y-intercept / gradient) - M