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 formula for the random uncertainty (Δd) can be calculated as the range of the measurements divided by the number of measurements (n):

$Δd = \frac{d_{max} - d_{min}}{n} = \frac{1.41 - 1.31}{5} = \frac{0.10}{5} = 0.020 \text{ m}$

First, we need to calculate the percentage uncertainty for each quantity:

1. For mass m:

   • Uncertainty: ±0.005 kg
   • Value: 0.20 kg
   • Percentage Uncertainty: $\% = \left( \frac{0.005}{0.20} \right) \times 100 = 2.5\%$

2. For height h:

   • Uncertainty: ±0.005 m
   • Value: 0.40 m
   • Percentage Uncertainty: $\% = \left( \frac{0.005}{0.40} \right) \times 100 = 1.25\%$

3. For mean distance d:

   • Uncertainty: ±0.02 m
   • Value: 1.37 m
   • Percentage Uncertainty: $\% = \left( \frac{0.02}{1.37} \right) \times 100 \approx 1.46\%$

From these calculations, mass m has the largest percentage uncertainty.

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

$E_p = mgh$

Substituting in:

• m = 0.20 kg
• g = 9.81 m/s²
• h = 0.40 m

Calculating:

$E_p = 0.20 \times 9.81 \times 0.40 = 0.784 \text{ J}$

Using the work-energy principle, the work done by friction (W) is equal to the change in potential energy:

$W = F_f imes d$

Since all potential energy is converted to work done against friction:

$E_p = F_f \times d$

Rearranging gives:

$F_f = \frac{E_p}{d} = \frac{0.784}{1.37} \approx 0.57 \text{ N}$

One assumption made could be that there is no energy or heat loss on the ramp due to friction.