Question

You are seated in a small airplane. The child sitting next to you had been getting a bit loud, so you are letting him sit in your lap so he will be quiet. Your inertia is 60kg, the child’s inertia is 15kg, and the plane’s inertia is 10000kg. All of a sudden, the plane hits an air pocket and begins to drop at |a| = 1.5m/s 2 . (Only for a short time, everyone gets out of this okay.)

(a)Draw free-body diagrams for the vertical forces on the child, yourself, and the airplane, labelling the forces using the F type by,on notation introduced in the reading and in lab. Make sure the lengths of the force vectors are appropriate for the magnitudes of the forces. Make a notation if you must draw one to a different scale.
(b)Identify all the forces that form interaction pairs.
(c)Find the magnitudes of the forces. Show your work, or explain briefly how you obtained these magnitudes. (d)When would you feel "heavier", when the plane is accelerating downward, or after it has levelled off again? Briefly explain your answer.

Answer 1

Answer:

N₁ = 222 N ,  N₂ = 1035 N ,   N₃ = 148735 N

Explanation:

See the attachment for parts a and b

c) Let's use Newton's second law for each body, let's start with the child

      N₁- W_child = m₁ a

      N₁ = m₁ a + W_child

     N₁ = m₁ (a + g)

Where m₁ is the child's masses

      N₁ = 15 (5 + 9.8)

      N₁ = 222 N

For the woman

      N₂ –W_child - W-woman = m₂ a

Where m₂ is the woman's mass

      N₂ = m₂ a + m₂ g + m₁ g

      N₂ = 60 5 + 9.8 (60 +15)

      N₂ = 1035 N

For the plane

      N₃ - W_child - W_woman - W_plane = m₃ a

Where m₃ is the mass of the plane

       N₃ = m₃ a + g (m₁ + m₂ + m₃)

       N₃ = 10000 5 + 9.8 (15 + 60 + 10000)

       N₃ = 148735 N

d) when the plane accelerates down the two accelerations are in the same direction, which is why, when the plane accelerates upwards the two accelerations and are subtracted, this is the force that the plane exerts on the child. The feeling of weight that is the force that the child applies against the plane is higher when it accelerates upwards.