Momentum with respect to external Forces: Difference between revisions
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Claimed by vkt3 | Claimed by vkt3 | ||
==The Main Idea== | ==The Main Idea== | ||
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==Examples== | ==Examples== | ||
Standing on Earth, you throw a small rock with a mass of 0.5 kg into the air. At the instant it leaves your hand, the rock's velocity is < | Standing on Earth, you throw a small rock with a mass of 0.5 kg into the air. At the instant it leaves your hand, the rock's velocity is v=<0.1,4.0,0.3> m/s Ignore air resistance. | ||
a. Initial Momentum? | a. Initial Momentum? | ||
m=0.5, v=<0.1,4,0.3> p=<0.05,2,0.15> kgm/s | |||
b.Rock's momentum after 0.25 seconds? | |||
pf=pi+Fnet(deltat) | |||
== | pf=<0.05,2,0.15>+<0,(-9.8)(0.5),0>(0.25)=<0.05,2,0.15>+<0,-1.225,0>=pf | ||
pf=<0.05,0.775,0.15> kgm/s | |||
c.Calculate the average velocity of the rock from just after it leaves your hand to 0.25 seconds later. | |||
p=mv, v=p/m | |||
== | vf=(pf/m)=(1/0.5)<0.05,0.775,0.15>=vf | ||
vf=<0.1,1.55,0.3>m/s | |||
vavg=(vi+vf)/2 = (0.5)*[<0.1,4,0.3> + <0.1,1.55,0.3>]= (0.5)<0.2,5.55,0.6>= | |||
vavg=<0.1,2.775,0.3>m/s | |||
d. If a rock's initial position just as it leaves your hand is <0,1.2,0>m, find the vector position of the ball after 0.25 seconds. | |||
=== | ri=<0,1.2,0>m | ||
rf=ri+vavg(deltat)= <0,1.2,0>+<0.1,2.775,0.3>(0.25)= | |||
<0,1.2,0>+<0.025,0.694,0.075>= | |||
rf=<0.025,1.894,0.075> | |||
==Connectedness== | |||
This topic is the basis behind calculating most forms of linear movement with simple forces. While a simple formula, this equation is a powerful tool as that it can include any number of forces acting on a system, and show the change in momentum of an object. | |||
This equation can be used to calculate the simple movements of objects in the vacuum of space with respect to the magnitude of forces acting upon the system. | |||
==History== | |||
The Momentum Principle was born from Newton's First Law which states that an object at rest will remain at rest, and an object in motion will remain in motion unless acted upon by an external force. | |||
[[Category: | [[Category:Momentum Principle]] | ||
Revision as of 22:30, 6 December 2015
Claimed by vkt3
The Main Idea
Momentum in an open system, is fundamentally different from that within a closed system. No longer do individual elements of a system's momentum equal to each other symettrically to add up to 0, however, they will have to even out to the magnitude of the added Force.
A Mathematical Model
They equation expressing this idea is [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
Standing on Earth, you throw a small rock with a mass of 0.5 kg into the air. At the instant it leaves your hand, the rock's velocity is v=<0.1,4.0,0.3> m/s Ignore air resistance.
a. Initial Momentum? m=0.5, v=<0.1,4,0.3> p=<0.05,2,0.15> kgm/s
b.Rock's momentum after 0.25 seconds? pf=pi+Fnet(deltat)
pf=<0.05,2,0.15>+<0,(-9.8)(0.5),0>(0.25)=<0.05,2,0.15>+<0,-1.225,0>=pf pf=<0.05,0.775,0.15> kgm/s
c.Calculate the average velocity of the rock from just after it leaves your hand to 0.25 seconds later. p=mv, v=p/m
vf=(pf/m)=(1/0.5)<0.05,0.775,0.15>=vf vf=<0.1,1.55,0.3>m/s vavg=(vi+vf)/2 = (0.5)*[<0.1,4,0.3> + <0.1,1.55,0.3>]= (0.5)<0.2,5.55,0.6>= vavg=<0.1,2.775,0.3>m/s
d. If a rock's initial position just as it leaves your hand is <0,1.2,0>m, find the vector position of the ball after 0.25 seconds.
ri=<0,1.2,0>m rf=ri+vavg(deltat)= <0,1.2,0>+<0.1,2.775,0.3>(0.25)= <0,1.2,0>+<0.025,0.694,0.075>= rf=<0.025,1.894,0.075>
Connectedness
This topic is the basis behind calculating most forms of linear movement with simple forces. While a simple formula, this equation is a powerful tool as that it can include any number of forces acting on a system, and show the change in momentum of an object.
This equation can be used to calculate the simple movements of objects in the vacuum of space with respect to the magnitude of forces acting upon the system.
History
The Momentum Principle was born from Newton's First Law which states that an object at rest will remain at rest, and an object in motion will remain in motion unless acted upon by an external force.