Question

Кран поднимает тело массой 3 тонны на высоту 6 метров. Сколько бензина сгорит в двигателе, если его КПД равен 25%?

Answer 1

Кпд=m1*g*h/q*m2
m2=m1*g*h/q*кпд=3000*10*6/44*10^6*0,25=0,016 кг

Answer 2

Calculation of Fuel Consumption for Lifting a 3-Tonne Load

To calculate the amount of fuel burned by the engine to lift a 3-tonne load to a height of 6 meters, we can use the concept of work done and the efficiency of the engine.

Given: - Mass of the load (m) = 3 tonnes = 3000 kg - Height lifted (h) = 6 meters - Efficiency of the engine (η) = 25%

Calculation Steps:

1. Calculate the Work Done: The work done in lifting the load to a certain height is given by the formula: \[ \text{Work (W)} = \text{Force (F)} \times \text{Distance (d)} \] Here, the force required to lift the load is equal to the weight of the load, and the distance is the height lifted.

\[ \text{Work (W)} = \text{Force (F)} \times \text{Distance (h)} \] \[ \text{Work (W)} = \text{Mass (m)} \times \text{Acceleration due to gravity (g)} \times \text{Distance (h)} \]

Using the value of acceleration due to gravity (g) as 9.81 m/s²: \[ \text{Work (W)} = 3000 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 6 \, \text{m} \]

The work done is the energy required to lift the load to the given height.

2. Calculate the Fuel Consumption: The fuel consumption can be calculated using the efficiency of the engine. The work done is the input energy, and the actual energy consumed by the engine can be calculated using the efficiency.

\[ \text{Energy consumed by the engine} = \frac{\text{Work done}}{\text{Efficiency}} \]

Using the given efficiency of 25%: \[ \text{Energy consumed by the engine} = \frac{W}{\eta} \]

The energy consumed by the engine is directly related to the amount of fuel burned.

3. Final Calculation: The energy consumed by the engine can be converted to the amount of fuel burned based on the specific energy content of the fuel used.

Conclusion:

The amount of fuel burned by the engine to lift a 3-tonne load to a height of 6 meters, given an efficiency of 25%, can be calculated using the steps outlined above.