Question

1. A 30 kg child stands in an elevator that is accelerating upward at a rate of 1.5 m/s2.

Draw a free body diagram for the child.

Calculate the net force acting on the child.

Calculate the force between the child and the floor of the elevator.

Answer 1

a) Let's draw a free body diagram for the child:

b)Let's calculate the net force acting on the child. Applying the Newton's Second Law of Motion, we get:

$$F_{Net}=ma=30\ kg\cdot1.5\ \dfrac{m}{s^2}=45\ N.$$

c) The force between the child and the floor of the elevator (or the normal force) can be found as follows:

$$N-mg=ma,$$ $$N=m(g+a)=30\ kg\cdot(9.8\ \dfrac{m}{s^2}+1.5\ \dfrac{m}{s^2})=339\ N.$$