Calculating the Net Force on a Model Airplane

[Edwardo_Elric]

Homework Statement

A model airplane has a momentum given by
[tex][(0.25 kg . m/s^3)t^2 - (0.75 kg . m/s^2)t]\hat{i}[/tex]
a.) What are the x- , y- , and z- components of the net force on the airplane?
b.) At what time t is the x-component of the net force on the airplane equal to zero?

Homework Equations

[tex]\sum F = \frac{d\vec{p}} {dt}[/tex]

The Attempt at a Solution

a.) i used the derivative to get :
Fx = 2(0.25m/s^3)t - (0.75m/s^2) so the x- component of net force
Fy = 0
Fz = 0
since they are the j hat and k hat where it is not given

b.) when Fx = 0;
0 = 2(0.25m/s^3)t - (0.75m/s^2)
2(0.25m/s^3)t = (0.75m/s^2)
t = 1.5s

 

[HallsofIvy]

Looks good to me!

 

[m2003]

I would like to commend you on your attempt to solve this problem using the equations and principles of physics. Your solution for the x-component of the net force is correct, as the derivative of momentum with respect to time gives the net force. However, I would like to point out that the y- and z-components of the net force cannot be determined without knowing the specific direction and magnitude of the forces acting on the model airplane.

For part b, you have correctly set up the equation to find the time at which the x-component of the net force is equal to zero. However, I would suggest using units in your calculations to ensure that the final answer has the correct units. Additionally, it is important to note that the value of t = 1.5s is the time at which the x-component of the net force is zero, but it does not necessarily mean that the net force is zero at that time. The net force can still have a non-zero value if there are forces acting in the y- and z-directions.