Question 23M.3.HL.TZ2.1
| Date | May 2023 | Marks available | [Maximum mark: 11] | Reference code | 23M.3.HL.TZ2.1 |
| Level | HL | Paper | 3 | Time zone | TZ2 |
| Command term | Calculate, Deduce, Explain, Plot, State | Question number | 1 | Adapted from | N/A |
A student investigates the relationship between the pressure in a ball and the maximum force that the ball produces when it rebounds.
A pressure gauge measures a difference Δp between the atmospheric pressure and the pressure in the ball. A force sensor measures the maximum force Fmax exerted on it by the ball during the rebound.
State one variable that needs to be controlled during the investigation.
[1]
height «of drop» OR velocity «of ball» OR kinetic energy «of ball» OR temperature/mass/radius/surface area/volume of ball ✓
Allow reference to controlling spin on the ball
Do not accept bald temperature, mass, surface area or volume.
The student collects the following data.
| Gauge pressure Δp / kPa | Maximum force Fmax / N |
| 10 | 108 |
| 20 | 133 |
| 30 | 158 |
| 40 | 170 |
| 50 | 188 |
| 60 | 192 |
| 70 | 206 |
| 80 | 220 |
The student initially hypothesizes that Fmax is proportional to Δp.
Deduce, using two suitable data points from the table, that the student’s initial hypothesis is not supported.
[3]
refers to 2 non-adjacent points ✓
suitable calculation to analyze the proportionality ✓
identifies variation/difference in calculated values, «thus hypothesis not supported» ✓
Award full marks if more than two points used appropriately.
Allow [2 max] if they use at least three points to show that two increments in force are not consistent with the corresponding increments in pressure and therefore it is not a straight line.
The student now proposes that = kΔp.
The student plots a graph of the variation of with Δp.
State the unit for k.
[1]
N2 m2 OR kg2 m4 s−4 OR N3 Pa−1 ✓
Award [0] if they convert to base units incorrectly.
Plot on the graph the position of the missing point for the Δp value of 40 kPa.
[1]
point plotted at (40 kPa, 49 × 105 N3) ✓
Allow for the point to be plotted from 46 to 56 × 105 N3 at 40 kPa, as candidates may calculate or may plot from a graphical analysis.
The percentage uncertainty in Fmax is ±5 %. The error bars for at Δp = 10 kPa and Δp = 80 kPa are shown.
Calculate the absolute uncertainty in for Δp = 30 kPa. State an appropriate number of significant figures for your answer.
[3]
15 % seen anywhere ✓
«Δ(F3) =» 39.4 × 105 × 0.15 = 5.9 × 105 ✓
±6 × 105 ✓
MP1 is for the propagation of 5 %. It can be shown differently, e.g. 3 × 5% Allow students to use 40 × 105 (from the graph).
Award MP3 for any uncertainty rounded to 1 significant digit
Award [3] for a BCA.
Allow ECF from MP1 and MP2
Plot the absolute uncertainty determined in part (d)(i) as an error bar on the graph.
[1]
error bar drawn at 30 kPa from 34 × 105 to 46 × 105 N3 ✓
Allow ± half square on each side of the bar or one square overall (± 2 × 105)
Allow ECF from d(i).
Explain why the new hypothesis is supported.
[1]
a «straight» line can be drawn that passes through origin ✓