A uniform chain 10m long and weighing 6 kg permetre hangs vertically.calculate the work required to wind it up..
Plzz solve it
Well, let me break it down for you. If the chain is hanging vertically, that means it's already down, right? So why would you want to wind it up? Are you trying to give it a whirl and see if it can do a little dance? Because that would be quite a sight!
But let me not be a clown about this. If you want to calculate the work required to wind up the chain, we need to consider the weight of the entire chain. Since the chain weighs 6 kg per meter, and it is 10 meters long, we can calculate the total weight of the chain as 6 kg/m x 10 m = 60 kg.
To find the work required to wind up the chain, we need to multiply the weight of the chain by the distance it needs to be lifted. Assuming you want to lift the entire chain vertically, the distance would be equal to the length of the chain, which is 10 meters.
Now, work is calculated as the product of force and distance. The force in this case is the weight of the chain, which is 60 kg. The distance is 10 meters.
So, the work required to wind up the chain would be 60 kg x 10 m = 600 kg·m.
There you have it! The work required to wind up the chain is 600 kg·m, or kilogram meters. But remember, laughter can be the best source of energy, so maybe a good joke or two could also help in winding up that chain!
To calculate the work required to wind up the chain, we need to determine the potential energy stored in the chain when it is lifted.
The potential energy of an object at a height h is given by the equation:
Potential Energy = Mass * Gravity * Height
In this case, the height is equal to the length of the chain (10m) and the mass is given by the product of the weight per meter (6 kg/m) and the length of the chain (10m).
Mass = Weight per meter * Length
Let's calculate the mass first:
Mass = 6 kg/m * 10 m = 60 kg
Now we can calculate the potential energy:
Potential Energy = Mass * Gravity * Height
Potential Energy = 60 kg * 9.8 N/kg * 10 m
Potential Energy = 5880 J
Therefore, the work required to wind up the chain is 5880 joules.
To solve this problem, we can use the concept of work done against gravity. The work required to wind up the chain is equal to the potential energy gained by the chain.
First, we need to find the mass of the chain. We know that the chain weighs 6 kg per meter and the total length of the chain is 10 meters. Therefore, the mass of the chain can be calculated as:
mass = weight per meter * length
= 6 kg/m * 10 m
= 60 kg
Next, we need to find the height to which the chain is lifted in order to calculate the potential energy gained. Since the chain is hanging vertically, the height lifted will be equal to the length of the chain, which is 10 meters.
Now, we can calculate the potential energy gained, which is equal to the work done:
potential energy = mass * acceleration due to gravity * height
= 60 kg * 9.8 m/s^2 * 10 m
= 5880 J
Therefore, the work required to wind up the chain is 5880 Joules.
integrate from x = 0 to x = 10
dm/dx = 6 kg/m
F = x * 6 * 9.81
d work = F(x) dx
d work = x (6)(9.81) dx
= (x^2/2) * 6 * 9.81 from 0 to 10
=(100/2)*6*9.81