Momentum from F in component form

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SUMMARY

The change in momentum of a particle subjected to a force defined by F = 26i – 12t²j can be calculated using the area under the force-time curve. This area represents the impulse imparted to the particle, which directly correlates to the change in momentum. To find this area between t = 1s and t = 2s, one must evaluate the integral of the force function over this interval. However, alternative methods exist for those not yet familiar with calculus.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Basic knowledge of momentum and impulse
  • Familiarity with force vectors in component form
  • Introductory calculus concepts, specifically integrals (optional)
NEXT STEPS
  • Study the relationship between force, impulse, and momentum
  • Learn how to calculate the area under a curve using basic geometric shapes
  • Explore numerical methods for approximating integrals
  • Review Newton's laws and their applications in physics problems
USEFUL FOR

Physics students, educators, and anyone interested in understanding the principles of force and momentum in mechanics.

EricHoffman
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I am having some trouble figuring out where to start with this problem:

The force on a particle of mass m is given by:

F= 26i – 12t^2j

where F is in N and t in seconds.

What will be the change in the particle’s momentum between t=1s and t=2s?

Can anyone point me in the right direction?

Thanks,
Eric
 
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The area under a force curve is equal to the change in momentum
 
OK, so maybe this is where I'm having difficulty. From what I can gather, figuring the area under a curve requires some knowledge of integrals; something I haven't got to yet in Calc class.

Is this assumption correct? Assuming it is, is there a way to do it without using integrals?

--Eric
 

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