A chain is held on a frictionless table with 1/3 of its length hanging over the edge. If the chain has length L = 33 cm and mass m = 21 g, how much work is required to pull the hanging part back onto the table?

0.11 m, so the center of mass of that part of the chain is 0.055 m below edge.

W = mgH = (0.021/3)kg*g*(0.055) = ____J

notice that the kg is different.

To find the work required to pull the hanging part of the chain back onto the table, we need to consider the potential energy of the hanging chain.

The potential energy of an object is given by the equation: Potential Energy = mass × acceleration due to gravity × height

In this case, the height of the hanging chain is 1/3 of its length. So, the height (h) is given by: h = (1/3) × L

The mass (m) of the hanging chain is given as 21 g. To convert this to kg, we divide by 1000: m = 21 g ÷ 1000 = 0.021 kg

The acceleration due to gravity (g) is approximately 9.8 m/s^2.

Now, we have all the values needed to calculate the potential energy. The formula becomes:
Potential Energy = (mass × acceleration due to gravity × height)

Potential Energy = (0.021 kg × 9.8 m/s^2 × (1/3) × 0.33 m)

Simplifying the equation:
Potential Energy = (0.021 × 9.8 × (1/3) × 0.33) = 0.021 J (to three significant figures).

Therefore, the work required to pull the hanging part of the chain back onto the table is approximately 0.021 Joules.

11 cm = 0.11 m hung over the edge, and the center of mass of that part of the chain was 0.055 m below the edge.

The work required to lift it all onto the table would be

W = m g H =
0.021 kg*g*(0.055 m) = ___ joules

asdasd123123