A uniform chain 10m long and weighing 6 kg permetre hangs vertically.calculate the work required to wind it up
Well, to wind up a chain, you'll need a little more than just a sense of humor! Let's get to the calculations, shall we?
Since the chain is hanging vertically, the work required to wind it up can be found by multiplying the weight of the chain by the distance it needs to be raised.
The weight of the chain is given as 6 kg/metre, and the distance it needs to be raised is 10 metres. So, the total weight of the chain is 6 kg/metre * 10 metres = 60 kg.
Now, to calculate the work, we need to use the formula: Work = Force × Distance.
The force here is the weight of the chain, which we just found to be 60 kg. The distance is the same 10 metres.
So, the work required to wind up the chain is: Work = 60 kg × 10 metres = 600 kg·m.
However, since work is usually measured in joules, we need to convert kg·m to joules. One joule is equal to one newton-meter, and since weight is the force, we can convert from kg·m to joules by multiplying by the acceleration due to gravity (9.8 m/s^2).
Converting 600 kg·m to joules: 600 kg·m × 9.8 m/s^2 = 5880 joules.
Therefore, the work required to wind up the chain is approximately 5880 joules.
And remember, winding up a chain may be hard work, but it's definitely worth the "lift" of accomplishment!
To calculate the work required to wind up the chain, we need to consider the weight of the chain and the distance it needs to be lifted.
Given:
- Length of the chain (L) = 10 m
- Weight of the chain per unit length (w) = 6 kg/m
To calculate the total weight of the chain (W), we multiply the weight per unit length by the total length of the chain:
W = w * L
W = 6 kg/m * 10 m
W = 60 kg
The work required to lift the chain is given by the formula:
Work (W) = Force (F) * Distance (d)
In this case, the force is equal to the weight of the chain (W), and the distance is equal to the total length of the chain (L).
Work (W) = W * L
Work (W) = 60 kg * 10 m
Work (W) = 600 kg·m^2/s^2
The unit for work is Joules (J), hence we can express the work required as:
Work (W) = 600 J
Therefore, the work required to wind up the chain is 600 Joules.
To calculate the work required to wind up the uniform chain, we need to consider two factors: the gravitational potential energy and the work done against gravity.
Let's break down the problem step by step:
1. Determine the height the chain needs to be lifted to wind it up completely.
- Since the chain hangs vertically, the entire length of the chain needs to be lifted.
- Given that the chain is 10m long, the height to which it needs to be lifted is also 10m.
2. Calculate the gravitational potential energy of the chain.
- The formula for gravitational potential energy is: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
- In this case, we need to find the potential energy of the entire chain (not just one meter of it), so we need to multiply the mass per meter by the length of the chain.
- The mass per meter is given as 6 kg/m, and the height is 10m.
- Substitute these values into the formula: PE = (6 kg/m * 10m) * 9.8 m/s^2.
- Calculate the result: PE = 588 J.
3. Determine the work done against gravity.
- The work done against gravity is equal to the gravitational potential energy.
- In this case, the work done against gravity is 588 J.
So, the work required to wind up the uniform chain is 588 J.
W = M g (L/2)= 294 J
The 1/2 factor comes about because the center of mass only has to be raised half the length