A helicopter lifts a 85 kg astronaut 19 m vertically from the ocean by means of a cable. The acceleration of the astronaut is g/11. How much work is done on the astronaut by (a) the force from the helicopter and (b) the gravitational force on her? Just before she reaches the helicopter, what are her (c) kinetic energy and (d) speed?

a) , b) , c) , d)

Explanation:

a) The equation of equilibrium for the astronaut is:

The expression for the force from the helicopter is:

The work done by the force is:

b) The work done by the gravitational force on the astronaut is:

d) The speed before the astronaut reaches the helicopter is:

c) The kinetic energy of the astronaut before reaching the helicopter is:

Which is equal to the net work on the astronaut.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach