Calculating the Net Force on a Model Airplane

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SUMMARY

The net force on a model airplane is calculated using the momentum equation given by [(0.25 kg . m/s^3)t^2 - (0.75 kg . m/s^2)t] in the x-direction. The x-component of the net force is determined to be Fx = 2(0.25 m/s^3)t - (0.75 m/s^2), while the y- and z-components are both zero. The x-component of the net force equals zero at t = 1.5 seconds, confirming the calculations are accurate.

PREREQUISITES
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  • Familiarity with Newton's second law of motion
  • Basic calculus for differentiation
  • Knowledge of vector components in physics
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  • Learn about vector calculus and its role in physics
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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
 
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