Какова средняя выработка энергии двигателя транспортера, который равномерно поднимает 900 тонн щебня на высоту 6

Sofya

14

Let"s solve this problem step by step.

1. First, let"s determine the work done by the conveyor in lifting the gravel. The work done is calculated using the formula:

\[ \text{Work} = \text{Force} \times \text{Distance} \]

In this case, the force is the weight of the gravel being lifted, and the distance is the height the gravel is raised. The weight of the gravel can be calculated using the formula:

\[ \text{Weight} = \text{Mass} \times \text{Acceleration due to Gravity} \]

Given that the mass of the gravel is 900 tons and the acceleration due to gravity is \(9.8 \ m/s^2\), we can calculate the weight as follows:

\[ \text{Weight} = 900 \ \text{tons} \times 9.8 \ \text{m/s}^2 \]

2. Next, we need to convert the weight from tons to kilograms, as the standard unit for mass in the International System of Units (SI) is kilograms. One ton is equal to 1000 kilograms, so we can convert the weight as follows:

\[ \text{Weight (in kg)} = 900 \ \text{tons} \times 1000 \ \text{kg/ton} \]

3. Now that we have the weight in kilograms, we can calculate the work done by the conveyor:

\[ \text{Work} = \text{Weight} \times \text{Distance} \]

Given that the distance is 6 meters, we can calculate the work as follows:

\[ \text{Work} = \text{Weight (in kg)} \times 6 \ \text{m} \]

4. Finally, we can calculate the average power output of the conveyor over the given time interval. Power is defined as the work done per unit of time:

\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \]

Given that the time interval is 30 minutes, which is equivalent to 1800 seconds, we can calculate the power as follows:

\[ \text{Power} = \frac{\text{Work}}{1800 \ \text{s}} \]

Now, let"s calculate the values:

1. Calculating the weight:

\[
\text{Weight} = 900 \ \text{tons} \times 9.8 \ \text{m/s}^2
\]

2. Converting the weight to kilograms:

\[
\text{Weight (in kg)} = 900 \ \text{tons} \times 1000 \ \text{kg/ton}
\]

3. Calculating the work:

\[
\text{Work} = \text{Weight (in kg)} \times 6 \ \text{m}
\]

4. Calculating the power:

\[
\text{Power} = \frac{\text{Work}}{1800 \ \text{s}}
\]

Now, let"s plug in the values and calculate the results.