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High School Physics: Calculate Fuel Consumption Rate per 100 km from Given Formulas
Physics
High School Grade 10-11
Question Content
1. Develop a formula for the fuel consumption rate per 100 km using the given relations: \(N = Q + W_p\), where \(N\) is total fuel, \(Q\) is fuel for idling per day, \(W_p\) is fuel for city driving work. The given calculation example is \(Q_{в} = \frac{1}{24} \left( \frac{42.9}{34} + \frac{40.9}{1.35} + 3 + 0.54 + 98.49 \right) \times 2\) for a 3 km distance, with prior formulas \(b_{тр} = \frac{t_n \cdot V_n + t_d V_d}{V_n + V_m}\) where \(t_n, t_d\) are time values for different driving modes.
Correct Answer
The final fuel consumption rate per 100 km is approximately 29.33 L/100km
Detailed Solution Steps
1
Step 1: Calculate the values inside the parentheses first. Compute each fraction: \(\frac{42.9}{34} \approx 1.262\), \(\frac{40.9}{1.35} \approx 30.296\)
2
Step 2: Sum all the terms inside the parentheses: \(1.262 + 30.296 + 3 + 0.54 + 98.49 = 133.588\)
3
Step 3: Multiply the sum by 2 and divide by 24: \(Q_{в} = \frac{1}{24} \times 133.588 \times 2 = \frac{267.176}{24} \approx 11.132\) liters for 3 km
4
Step 4: Scale the 3 km fuel consumption to 100 km: \(\text{Consumption per 100 km} = 11.132 \times \frac{100}{3} \approx 29.33\) L/100km
Knowledge Points Involved
1
Fuel Consumption Rate Calculation
This refers to the measurement of fuel used per unit distance (typically 100 km for automotive use). It involves aggregating fuel used for different driving modes (idling, moving) and scaling the value to a standard distance for consistent comparison. Used to evaluate vehicle efficiency and operational costs.
2
Algebraic Formula Derivation for Engineering Physics
This involves combining physical relationships (total fuel = idle fuel + driving fuel) to create a calculable formula for a specific parameter (fuel per 100 km). It requires substituting known values and simplifying arithmetic expressions to solve for the target variable, common in automotive and mechanical engineering problems.
3
Unit Scaling for Physical Quantities
This is the process of converting a measured physical quantity (fuel used for 3 km) to a standard unit or reference scale (fuel used for 100 km). It uses proportionality: if \(x\) fuel is used for \(d\) km, then fuel for 100 km is \(x \times \frac{100}{d}\), essential for creating standardized, comparable metrics.
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