The figure above shows a chain being held on a table with one quarter of its length hanging over the edge. Friction is negligible. The chain has length L = 24 cm and mass m = 0.012 kg. Calculate how much work is required to pull the hanging section back onto the table.
To calculate the work required to pull the hanging section of the chain back onto the table, we need to consider the potential energy of the chain.
The potential energy of an object is given by the formula:
Potential Energy = mass * gravitational acceleration * height
In this case, the height is equivalent to the length of the hanging section of the chain that needs to be lifted back onto the table.
To calculate the height, we need to determine the length of the hanging section. Given that one quarter of the length of the chain is hanging off the table, the length of the hanging section is:
Length of hanging section = 1/4 * Length of chain
Length of hanging section = 1/4 * 24 cm
Length of hanging section = 6 cm
Now, we can calculate the potential energy:
Potential Energy = mass * gravitational acceleration * height
Potential Energy = 0.012 kg * 9.8 m/s^2 * (6 cm / 100 cm) [converting cm to meters]
Potential Energy = 0.012 kg * 9.8 m/s^2 * 0.06 m
Potential Energy = 0.007056 J
Therefore, the work required to pull the hanging section of the chain back onto the table is approximately 0.007056 Joules.