Calculate the height through which a crane can lift a load of 4t , when its motor of 4HP operates for 10s. [Take g=10N/kg ]
1 HP = 745.6999 W
4 HP = 2982.7996 W
4t = 4000 kg
Use
mgh=PΔt
h=PΔt/mg
=2982.7996*10/(4000*10)
=0.75m approximately
To calculate the height through which the crane can lift the load, we can use the concept of work and power. The work done by the motor can be determined using the formula:
Work = Power × Time
The power can be calculated using the formula:
Power = Force × Velocity
First, let's calculate the power:
Given:
Power = 4 HP
Since 1 HP is equal to 746 Watts, we can convert the power to Watts:
Power = 4 × 746 = 2984W
Next, we calculate the work done:
Given:
Time = 10s
Work = Power × Time
Work = 2984W × 10s
Work = 29840 Joules
Now, we can determine the height through which the load can be lifted using the formula:
Work = Force × Distance
Rearranging the formula, we can solve for distance:
Distance = Work / Force
Given:
Force = 4t = 4 × 1000kg = 4000kg = 40000N
Distance = 29840 Joules / 40000 N
Distance = 0.746 meters
Therefore, the crane can lift the load through a height of approximately 0.746 meters.
To calculate the height through which a crane can lift a load, we need to determine the work done by the crane's motor.
The work done is given by the formula:
Work = Force x Distance
In this case, the force is the weight of the load, which is 4 tonnes or 4000 kg. The distance is the height through which the load is lifted, which we need to find.
Since we have the power of the motor (4 HP) and the time it operates (10 seconds), we can relate power, work, and time using the following formula:
Power = Work / Time
First, let's convert the power from horsepower to watts:
1 HP is approximately equal to 746 watts. So, 4 HP is equal to 4 x 746 = 2984 watts.
Now, rearrange the formula to solve for work:
Work = Power x Time
Substitute the values we have:
Work = 2984 watts x 10 seconds = 29,840 joules
Next, substitute the work and force into the work formula:
Work = Force x Distance
29,840 Joules = 4000 kg x g x Distance
Where g is the acceleration due to gravity, which is given as 10 N/kg.
Solve for Distance:
Distance = (29,840 Joules) / (4000 kg x 10 N/kg)
Distance = 0.746 meters
Therefore, the height through which the crane can lift a load of 4 tonnes, when its motor operates for 10 seconds, is approximately 0.746 meters.