Question

Подъемный кран равномерно поднимает груз массой 3 тонны за 0,5 мин. Мощность подъемного крана 10 кВт. Какую работу совершает кран ? Чему равна высота, на которую поднимается груз? Со всеми формулами пожалуйста.

Answer 1

A=mgh; N=A/t =>N= mgh/t из этого выразим h: Nt/mg.

Answer 2

Calculation of Work Done by the Crane

To calculate the work done by the crane, we can use the formula:

Work = Power x Time

Given that the power of the crane is 10 kW and the time taken to lift the load is 0.5 minutes, we can substitute these values into the formula:

Work = 10 kW x 0.5 min

To perform the calculation, we need to convert the time from minutes to seconds, as power is measured in watts (W) and time is measured in seconds (s). There are 60 seconds in a minute, so:

Work = 10,000 W x 30 s

Now we can calculate the work done by the crane:

Work = 300,000 joules (J)

Therefore, the crane performs 300,000 joules of work.

Calculation of the Height to Which the Load is Lifted

To calculate the height to which the load is lifted, we can use the formula:

Work = Force x Distance

Given that the mass of the load is 3 tons (which is equivalent to 3000 kg) and the work done by the crane is 300,000 J, we can substitute these values into the formula:

300,000 J = Force x Distance

The force can be calculated using the formula:

Force = Mass x Gravity

Where gravity is approximately 9.8 m/s^2.

Force = 3000 kg x 9.8 m/s^2

Now we can calculate the force:

Force = 29,400 N

Substituting the force into the previous equation:

300,000 J = 29,400 N x Distance

Solving for distance:

Distance = 300,000 J / 29,400 N

Now we can calculate the height to which the load is lifted:

Distance = 10.2 meters

Therefore, the load is lifted to a height of 10.2 meters.

Please note that the calculations provided are based on the information given and may not account for all real-world factors or variables.