The position of a 2.75x10^5 N training helicopter under test is given by

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Homework Help Overview

The problem involves determining the net force acting on a training helicopter based on its position vector, which is expressed as a function of time. The subject area pertains to dynamics and kinematics, specifically the relationship between position, velocity, acceleration, and force.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the necessity of taking the second derivative of the position vector to find acceleration. There is a focus on understanding the relationship between position, velocity, and acceleration, as well as how these relate to calculating net force using Newton's second law.

Discussion Status

The discussion is exploring the reasoning behind the mathematical steps needed to find the net force. Some participants express understanding of the concepts involved, while others seek clarification on the derivation process. Guidance has been provided regarding the relationship between derivatives and physical quantities.

Contextual Notes

Participants are working under the constraints of a homework assignment, which specifies the need to express answers in terms of unit vectors and significant figures. There is an emphasis on the definitions and relationships between physical quantities without providing a complete solution.

Mdhiggenz
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Homework Statement



The position of a 2.75x10^5 N training helicopter under test is given by...?
vector r = (0.020m/s^3)t^3ihat+(2.2 m/s)tjhat-(0.060m/s^2)t^2 khat

Find the net force on the helicopter at t=5.0s

Express your answer in terms of ihat, jhat , and khat . Express your coefficient using two significant figures.


Homework Equations





The Attempt at a Solution



I don't understand why me must take the second derivative, already solved it just want some clarification on to why we get the second derivative.

Thank you!
 
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Mdhiggenz said:

Homework Statement



The position of a 2.75x10^5 N training helicopter under test is given by...?
vector r = (0.020m/s^3)t^3ihat+(2.2 m/s)tjhat-(0.060m/s^2)t^2 khat

Find the net force on the helicopter at t=5.0s

Express your answer in terms of ihat, jhat , and khat . Express your coefficient using two significant figures.


Homework Equations





The Attempt at a Solution



I don't understand why me must take the second derivative, already solved it just want some clarification on to why we get the second derivative.

Thank you!


By definition, the second derivative of position with respect to time is the acceleration. This should be pretty intuitive:

velocity is the rate of change of position with time.

acceleration is the rate of change of velocity with time.

Hence, velocity is the derivative of position, and acceleration is the derivative of velocity.
 
I think I understand, since force = sigmaF = Ma

we have the force, and we are solving for the acceleration in order to multiply it by the mass to get the net?
 
Mdhiggenz said:
I think I understand, since force = sigmaF = Ma

we have the force, and we are solving for the acceleration in order to multiply it by the mass to get the net?

Yes, exactly. If you know the acceleration, and the mass, then you know the net force. That is because of Newton's 2nd Law.
 

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