Calculate the height through which a crane can lift a load of 4 ton when it's motor of 4 H.P operates for 10 sec. Acceleration due to gravity is 10 m/s2
To calculate the height through which the crane can lift a load, we need to take into consideration the work done and the potential energy gained.
First, let's find the work done by the motor of the crane. The work done is given by the equation:
Work = Power x Time
The power of the motor is given as 4 horsepower (H.P). We need to convert it to watts because the standard unit of power is watt.
1 horsepower (H.P) = 745.7 watts
So, the power of the motor is:
Power = 4 H.P x 745.7 = 2982.8 watts
Next, we need to find the work done. The work done is the product of power and time, given that the time is 10 seconds.
Work = 2982.8 watts x 10 seconds = 29828 watts-seconds (or joules)
Now, let's calculate the potential energy gained by the load. The potential energy gained is given by the equation:
Potential Energy = Mass x Gravity x Height
Here, the mass is given as 4 tons. We need to convert it to kilograms because the standard unit of mass is kilogram.
1 ton = 1000 kilograms
So, the mass of the load is:
Mass = 4 tons x 1000 = 4000 kilograms
The acceleration due to gravity is given as 10 m/s².
Now, rearranging the equation for potential energy, we can solve for height:
Height = Potential Energy / (Mass x Gravity)
Substituting the values:
Height = 29828 / (4000 x 10)
Height = 29828 / 40000
Height = 0.7457 meters
Therefore, the crane can lift the load to a height of approximately 0.746 meters.