A chain of mass `m` and length `l` lies on a horizontal table. The chain is allowed to slide down gently from the side of the table. Find the speed of the chain at the instant when last link of the chain slides from the table. Neglect friction everywhere.
(a) the force from thelicopter and
(b) the gravitational force on her
(c ) What are speed ot the kinetic energy and.
(d) the speed of the astronaut just before she reaches the helicopter?

Explanation

To find the speed of the chain at the instant when the last link of the chain slides from the table, we can use the principle of conservation of energy. Here are the steps to solve the problem:

### Step 1: Understand the situation
The chain of mass \( m \) and length \( l \) is initially lying on a horizontal table. As the chain slides off the table, it descends under the influence of gravity.

### Step 2: Identify the change in gravitational potential energy
When the chain is fully on the table, the center of mass of the chain is at a height of \( 0 \). As the last link of the chain slides off the table, the center of mass of the chain descends by \( \frac{l}{2} \) (since the center of mass of a uniform chain is at its midpoint).

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