IB Physics Propagation of Uncertainties

In an experiment, a radio-controlled car takes 2.50 ± 0.05 s to travel 40.0 ± 0.1 m.

What is the car’s average speed and the uncertainty in this value?

• 16 ± 1m s^-1

• 16.0 ± 0.2 m s^-1

• 16.0 ± 0.4 m s^-1

• 16.00 ± 0.36 m s^-1

The resistance R of a resistor is determined by measuring the potential difference V across it and the current I in it. The value of R is then calculated using the equation

 $R=\frac{V}{I}$  .
The values measured are V = 1.00 ± 0.05 V and I = 0.50 ± 0.01 A. What is the % uncertainty in the value of R?

• 2.5 %

• 3.0 %

• 7.0 %

• 10.0 %

An experiment is carried out to measure the resistance of a wire.

The current in the wire is (1.0 ± 0.2) A and the potential difference across the wire is (8.0 ± 0.4) V.

What is the resistance of the wire and its uncertainty?

• (8.0 ± 0.2) Ω

• (8.0 ± 0.6) Ω

• (8 ± 1) Ω

• (8 ± 2) Ω

A thermometer can be read to an accuracy of ±0.5 °C. This thermometer is used to measure a temperature rise from 40 °C to 100 °C.

What is the percentage uncertainty in the measurement of the temperature rise?

• 0.5 %

• 0.8 %

• 1.3 %

• 1.7 %

What could reduce systematic errors?

• averaging a large number of measurements

• careful calibration of measuring instruments

• reducing the sample size

• repeating measurements

The power loss P in a resistor is usually calculated using the formula  $P=\frac{V^2}{R}$  
The percentage uncertainty in the potential difference V is 3 % and the percentage uncertainty in the resistance R is 2 %. What is the percentage uncertainty in P?

• 4 %

• 7 %

• 8 %

• 11 %