A1. Data analysis question.

A student performs an experiment with a paper toy that rotates as it falls slowly through the air. After release, the paper toy quickly attains a constant vertical speed as measured over a fixed vertical distance.

The aim of the experiment was to find how the terminal speed of the paper toy varies with its weight. The weight of the paper toy was changed by using different numbers of paper sheets in its construction.

The graph shows a plot of the terminal speed v of the paper toy (calculated from the raw data) and the number of paper sheets n used to construct the toy. The uncertainty in v for n =1 is shown by the error bar.

(a) The fixed distance is 0.75 m and has an absolute uncertainty of 0.01 m. The percentage uncertainty in the time taken to fall through the fixed distance is 5 %.

  • (i) Calculate the absolute uncertainty in the terminal speed of the paper toy for n = 6.
  • (ii) On the graph, draw an error bar on the point corresponding to n = 6.

(b) On the graph, draw a line of best-fit for the data points.

(c) The student hypothesizes that v is proportional to n. Use the data points for n = 2 and n = 4 from the graph opposite to show that this hypothesis is incorrect.

(d) Another student hypothesized that v might be proportional to n. To verify this hypothesis he plotted a graph of v2 against n as shown below.

Explain how the graph verifies the hypothesis that v is proportional to √n.


A2. In 1997 a high-speed car of mass 1.1*104 kg achieved the world land speed record. The car accelerated uniformly in two stages as shown in the table. The car started from rest.

Use the data to calculate the

(a) average acceleration of the car in stage 1.

(b) average net force required to accelerate the car in stage 2.

(c) total distance travelled by the car in 12 s.


A3. (a) Draw the complete diagram of the circuit that uses a potential divider, ammeter, voltmeter and cell to measure the current-voltage characteristics for component X.

(Question A3 continued)

(b) The graph shows the current-voltage characteristics for the component X.

Component X is now connected across the terminals of a cell of emf 2.0 V and negligible internal resistance. Use the graph to show that the resistance of X is 0.83 Ω.

(c) A resistor of constant resistance 1.0 Ω is connected in series with the cell in (b) and with X. Use the graph to deduce that the current in the circuit is 1.3 A.




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