Question SPM.1B.HL.TZ0.1
| Date | May Specimen-2023 | Marks available | [Maximum mark: 12] | Reference code | SPM.1B.HL.TZ0.1 |
| Level | HL | Paper | 1B | Time zone | TZ0 |
| Command term | Calculate, Describe, Determine, Outline, State, Suggest | Question number | 1 | Adapted from | N/A |
A group of students investigate the motion of a conducting ball suspended from a long string. The ball is between two vertical metal plates that have an electric potential difference V between them. The ball is touched to one plate so that it becomes electrically charged and is repelled from the plate. For a given potential difference, the ball bounces between the plates with a constant period.
The students vary V and measure the time T for the ball to move once from one plate to the other. The table shows some of the data.
V is provided by two identical power supplies connected in series. The potential difference of each of the power supplies is known with an uncertainty of 0.01 kV.
State the uncertainty in the potential difference V.
[1]
0.02 «kV» ✓
T is measured with an electronic stopwatch that measures to the nearest 0.1 s.
Describe how an uncertainty in T of less than 0.1 s can be achieved using this stopwatch.
[2]
by measuring the time for many bounces ✓
and dividing the result by the number of bounces ✓
The graph shows the variation of T with V. The uncertainty in V is not plotted.
Outline why it is unlikely that the relationship between T and V is linear.
[1]
it is not possible to draw a straight line through all the error bars ✓
Calculate the largest fractional uncertainty in T for these data.
[2]
T = 0.5 s ✓
«» 0.2 ✓
The students suggest the following theoretical relationship between T and V:
where A is a constant.
To verify the relationship, the variation of T with is plotted.
Determine A by drawing the line of best fit.
[3]
a best-fit line drawn through the entire range of the data ✓
large triangle greater than half a line or two data points on the line greater than half a line apart ✓
correct read offs consistent with the line, eg ✓
Accept answer in the range 3.8–4.2
State the units of A.
[1]
kV s ✓
The theoretical relationship assumes that the ball is only affected by the electric force.
Suggest why, in order to test the relationship, the length of the string should be much greater than the distance between the plates.
[2]
the angle between the string and the vertical should be very small «for any position of the ball» ✓
so that the tension in the string is «almost» balanced by the ball’s weight
OR
restoring force from the string / horizontal component of tension negligibly small «compared with electric force» ✓
OWTTE