Question

A model airplane has momentum given by p=[(-0.75kg.m/s3)t2 + (3.0kg.m/s)] i + (0.25kg.m/s2)t j. Find the components Fx, Fy, and Fz of the net force on the airplane.

Answer 1

`F_x` = -1.5t

`F_y` = 0.25

`F_(z)` = 0

Step-by-step explanation:

Given equation;

p = [(-0.75 kgm/s³)t² + (3.0 kgm/s)] i + (0.25 kgm/s²)t j.

From Newton's law, the rate of change of momentum of a body is the net force acting on that body. i.e

∑F =
`(dp)/(dt)` -----------(i)

Substitute the equation of p into equation (i) and differentiate with respect to t as follows;

∑F =
`(dp)/(dt)` =
`(d| [(-0.75)t^(2) + (3.0)] i + (0.25)t j|)/(dt)`

∑F =
`(dp)/(dt)` =
`[-1.5t + 0]i + 0.25j`

∑F =
`[-1.5t + 0]i + 0.25j`

But

∑F =
`F_xi + F_yj + F_zk`

Where;

`F_x, F_y, F_z` are the components of the net force in the x, y and z direction respectively.

=>
`F_xi + F_yj + F_zk` =
`[-1.5t + 0]i + 0.25j` =
`-1.5ti + 0.25j`

=>
`F_x` = -1.5t

=>
`F_y` = 0.25

=>
`F_(z)` = 0