A uniform steel chain 20 m long and with a mass of 5 kg per m, hangs vertically. Compute the work required to wind it up
The center of mass must be raised 10 m. The work required to do that is
(10 m)*(mass)*g = 10m*100kg*9.8 m/s^2 = 9800 Joules
To compute the work required to wind up the steel chain, we need to find the gravitational potential energy gained when the chain is lifted to its final position. The formula for gravitational potential energy is given by:
Potential Energy = mass × gravitational acceleration × height
In this case, the mass of the steel chain is given as 5 kg per meter, so for a 20-meter chain, the total mass would be:
Total mass = mass per meter × length
= 5 kg/m × 20 m
= 100 kg
The gravitational acceleration, usually denoted as "g," is approximately 9.8 m/s².
The height to which the chain is lifted vertically is the same as its length, which is 20 meters.
Using these values, we can calculate the potential energy:
Potential Energy = mass × gravitational acceleration × height
= 100 kg × 9.8 m/s² × 20 m
= 19600 J
Therefore, the work required to wind up the steel chain is 19600 Joules.