What is the Force Acting on a Particle with Changing Velocity?

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Homework Help Overview

The discussion revolves around a particle with a mass of 0.2 kg moving in the x-y plane under the influence of gravity and a time-varying force F. The velocity of the particle is expressed as a function of time, and the participants are exploring how to determine the force acting on the particle at a specific time, t = 2.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are considering whether to directly substitute t = 2 into the velocity equation to find F. There is discussion about the need for limits in the integral related to the force and the implications of integrating F with respect to time. Some participants are questioning the relationship between force and acceleration, particularly in the context of F = ma.

Discussion Status

The discussion is active, with participants offering various perspectives on how to approach the problem. Some guidance has been provided regarding differentiation of the velocity equation to find acceleration, and there is recognition of the need to consider the time dependence of the force.

Contextual Notes

There is an acknowledgment of potential confusion regarding the integration of force and the implications of the variable nature of F. Participants are also reflecting on the connection between force, mass, and acceleration in their reasoning.

Doonami
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Homework Statement


A 0.2 kg particle moves in the x-y plane under the action of its weight and a force F that varies with time. The velocity of the particle is given by the expression

[tex]\hat{v}[/tex] = 7.5(t2 + 3)[tex]\hat{i}[/tex] - (10/3)(t3 - 4)[tex]\hat{j}[/tex]


Homework Equations


mv1 + [tex]\sum[/tex][tex]\int[/tex]Fdt = mv2


The Attempt at a Solution


Am I crazy? Or Can I just plug in 't=2' into the given equation? I'm sceptical, because it seems too good to be true. It is asking for F at t = 2 and the effect of gravity seems to be accounted for in the vector equation.
 
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hmmm good question
i haven't seen this type of question before but if your using the equation you have stated it looks like there should be some limits to deal with the integral.
On second thought, if you integrate F dt, you would end up with Ft which happens to be impulse so to be honest it looks a little confusing.
Maybe plug in your value for t into the velocity equation and then your value for t into the equation you have with the integral and rearrange to find F?
good luck!
 
RoryP said:
hmmm good question
if you integrate F dt, you would end up with Ft which happens to be impulse so to be honest
You cannot say that because F depends on the variable t !

So integration of Fdt doesn't give you Ft. this would only be the case if F were independent of t.

Now, the OP's question is to calculate F at t=2 no ?

What's the connection between F and v if you know that F=ma (a : acceleration)

marlon
 
ahhh nuts this is true!
sorry to be no help!
 
a = dv/dt

So, from that I should differentiate the equation for v with respect to time. I can just do this for the individual components (i and j) right? This should yield . . .

ma = 0.2[ (15t)i - (10t2)j ]

multiplied by mass, then sub in t=2.
 
Doonami said:
a = dv/dt

So, from that I should differentiate the equation for v with respect to time. I can just do this for the individual components (i and j) right? This should yield . . .

ma = 0.2[ (15t)i - (10t2)j ]

multiplied by mass, then sub in t=2.
Good. This tells you the net force, now find F.
 

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