Answer: To raise one end of the chain to a height of 6 m, we need to lift a length of the chain equal to the height, which is 6 m. The mass of this length of chain can be found using the linear density of the chain, which is defined as the mass per unit length. Since the chain is uniform, we can find the linear density by dividing the total mass by the total length:
linear density = mass / length = 80 kg / 10 m = 8 kg/m
So the mass of the 6 m length of chain that needs to be lifted is:
mass = linear density * length = 8 kg/m * 6 m = 48 kg
To find the work required to lift this mass to a height of 6 m, we can use the formula:
work = force * distance * cos(theta)
where force is the gravitational force on the mass, distance is the height that the mass is lifted, and theta is the angle between the force and the direction of motion (which is 0 degrees in this case, since the force is acting in the same direction as the motion).
The gravitational force on the mass is given by:
force = mass * acceleration due to gravity = 48 kg * 9.81 m/s^2 = 470.88 N
So the work required is:
work = force * distance * cos(theta) = 470.88 N * 6 m * cos(0) = 2825.28 J
Therefore, the work required to raise one end of the chain to a height of 6 m is 2825.28 joules.
Explanation: