Question

1. each tire of a three-wheeled electric vehicle (tuk-tuk) has a \\(12\text{cm} \times 8\text{cm}\\) area touching the ground. the mass of the vehicle is \\(240\text{ kg}\\) and it carries a driver and passengers with a total mass of \\(180\text{ kg}\\). find the minimum pressure needed in the tires. (take \\(g = 10\text{ms}^{-2}\\)) (4-marks)

Explanation:

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<reasoning>

Calculate total mass and weight

Find the total mass \(M\) and total downward force \(F\).
\[
M = 240\text{ kg} + 180\text{ kg} = 420\text{ kg}
\]
\[
F = M \cdot g = 420\text{ kg} \times 10\text{ ms}^{-2} = 4200\text{ N}
\]

Calculate total contact area

Find the total area \(A\) of all three tires.
\[
A_{\text{one}} = 12\text{ cm} \times 8\text{ cm} = 96\text{ cm}^2 = 96 \times 10^{-4}\text{ m}^2
\]
\[
A = 3 \times A_{\text{one}} = 3 \times 96 \times 10^{-4}\text{ m}^2 = 0.0288\text{ m}^2
\]

Calculate minimum tire pressure

Apply the pressure formula \(P = \frac{F}{A}\).
\[
P = \frac{4200\text{ N}}{0.0288\text{ m}^2} \approx 145833.33\text{ Pa}
\]
\[
P \approx 1.46 \times 10^5\text{ Pa}
\]
</reasoning>

<answer>
\(1.46 \times 10^5\text{ Pa}\) (or \(145.83\text{ kPa}\))
</answer>

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Answer:

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<reasoning>

Calculate total mass and weight

Find the total mass \(M\) and total downward force \(F\).
\[
M = 240\text{ kg} + 180\text{ kg} = 420\text{ kg}
\]
\[
F = M \cdot g = 420\text{ kg} \times 10\text{ ms}^{-2} = 4200\text{ N}
\]

Calculate total contact area

Find the total area \(A\) of all three tires.
\[
A_{\text{one}} = 12\text{ cm} \times 8\text{ cm} = 96\text{ cm}^2 = 96 \times 10^{-4}\text{ m}^2
\]
\[
A = 3 \times A_{\text{one}} = 3 \times 96 \times 10^{-4}\text{ m}^2 = 0.0288\text{ m}^2
\]

Calculate minimum tire pressure

Apply the pressure formula \(P = \frac{F}{A}\).
\[
P = \frac{4200\text{ N}}{0.0288\text{ m}^2} \approx 145833.33\text{ Pa}
\]
\[
P \approx 1.46 \times 10^5\text{ Pa}
\]
</reasoning>

<answer>
\(1.46 \times 10^5\text{ Pa}\) (or \(145.83\text{ kPa}\))
</answer>

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