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.

= -1.5t

= 0.25

= 0

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 =       -----------(i)

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

∑F = =

∑F = =

∑F =

But

∑F =

Where;

are the components of the net force in the x, y and z direction respectively.

=> =   =

=> = -1.5t

=> = 0.25

=> = 0

50 inches should be the resultant vector

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.