A nurse is injecting a child with 30 x 103 kg of vaccine Wit

A nurse is injecting a child with 3.0 x 10^-3 kg of vaccine. With what magnitude of force (assumed constant) must the nurse push on the plunger of the syringe, if the speed of the vaccine coming out is 1.4 m/s and the length of the plunger\'s motion is 3.4 cm?

Solution

The work done by the plunger of the syringe is given by,

W = F x Distance

and the energy of the vaccine is kinectic.

F x distance = W = 1/2 m v^2

F = [1/2 m v^2] / distance

F = [1/2 x 3 x 10 ^-3 x 1.4^2] / 0.034

F = 6.17 kgf