2. A student uses the apparatus shown to investigate the force of friction between the wheels of a toy car and a carpet - Scottish Highers Physics - Question 2 - 2016

The random uncertainty can be calculated using the range of the measurements. The maximum distance is 1.41 m and the minimum is 1.31 m:

[ \text{Uncertainty} = \frac{1.41 - 1.31}{2} = \frac{0.10}{2} = 0.05 , \text{m} ]

To find the percentage uncertainty for each quantity:

1. Mass (m): [ \text{Percentage uncertainty} = \frac{0.005}{0.20} \times 100 = 2.5% ]

2. Height (h): [ \text{Percentage uncertainty} = \frac{0.005}{0.40} \times 100 = 1.25% ]

3. Mean Distance (d): [ \text{Percentage uncertainty} = \frac{0.05}{1.37} \times 100 \approx 3.65% ]

The largest percentage uncertainty is in the mean distance ( d ).

The potential energy (PE) can be calculated using the formula:

[ PE = mgh ]

Substituting the values:

[ PE = (0.20 , \text{kg})(9.81 , \text{m/s}^2)(0.40 , \text{m}) \approx 0.7848 , \text{J} ]

The force of friction can be calculated by using the work-energy principle. The work done against friction equals the change in kinetic energy:

Assuming that the potential energy converts entirely to kinetic energy before stopping:

[ F_{friction} = \frac{PE}{d} = \frac{0.7848 , \text{J}}{1.37 , \text{m}} \approx 0.573 , \text{N} ]

One assumption made in calculating the average force of friction is that all potential energy is converted to kinetic energy and that there are no other energy losses (such as air resistance or rolling resistance).