Calculate the power of a crane in watts which lifts a man of 100kg to a height of 10m in 20sec
m g h / t
1000
500
490
To calculate the power of a crane, we need to use the following formula:
Power (P) = Work (W) / Time (t)
First, let's calculate the work done by the crane. The work done in lifting an object is given by the formula:
Work (W) = Force (F) x Distance (d)
The force required to lift an object can be determined using Newton's second law of motion, which states that force (F) equals the mass (m) of an object multiplied by the acceleration due to gravity (g). In this case, the mass is given as 100kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Force (F) = mass (m) x acceleration due to gravity (g)
Now, we can find the force:
F = 100kg x 9.8 m/s^2
Next, we need to calculate the distance the crane lifts the man. In this case, the distance is given as 10m.
Now, we have all the necessary values to calculate the work done by the crane:
W = F x d
Finally, we can calculate the power using the formula:
P = W / t
Now, let's plug in the values and calculate the power:
Force (F) = 100kg x 9.8 m/s^2 = 980N
Work (W) = Force (F) x Distance (d) = 980N x 10m = 9800 J (Joules)
Power (P) = Work (W) / Time (t) = 9800 J / 20s = 490 W (Watts)
Therefore, the power of the crane is 490 Watts.