Physics 197 Lecture Notes - Lecture 4: Particle System, Euclidean Vector, Weighted Arithmetic Mean

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1 Sep 2015

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Physics 197 Full Course Notes

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System: a set of interacting particles having a well-de ned boundary that allows us to determine whether a given particle is inside or outside the system. Extended object: a material object with a well-de ned surface in space that de nes its boundary and encloses a nonzero volume. A system"s total momentum (vector ptotal) is the vector sum of the momenta of its constituent particles: (vector ptotal) = vector p1 + vector p2 + vector pn. Purpose: this equation de nes a system"s total momentum vector ptotal. Symbols: vector p1 + vector p2 + vector pn are the momenta of the system"s n particles. Note: this equation applies to systems of n extended objects, too. The momentum-transfer principle means that a system"s internal interactions only transfer momentum back and forth within the system and therefore cannot affect a system"s total momentum. Only external interactions can transfer momentum into or out of a system and thus change its total momentum.

Related Questions

In this problem, let us consider that the two moving objects undergo collision such that after the collision, the objects stick together and travel off as a single unit. This is totally inelastic form of collision.

You are probably familiar that "momentum is conserved" in an inelastic collision. Solve the questions given below to clarify the meaning and implications of "momentum is conserved."

1)What physical quantities are conserved in this type of inelastic collision?
a) the magnitude of the momentum only
b) the net momentum (considered as a vector) only
c) the momentum of each object considered individually

2) Two cars of equal mass collide inelastically and stick together after the collision. Before the collision, their speeds are V1 and V2 . What is the speed of the two-car system after the collision?
a) V1+V2
b) V1-V2
c) V2-V1
d)(V1V2)^(1/2)
e) (1/2)(V1+V2)
f)(V1+V2)^(1/2)
g)The answer depends on the directions in which the cars were moving before the collision.

3) Two cars collide inelastically and stick together after the collision. Before the collision, the magnitudes of their momenta are P1 and P2 . After the collision, what is the magnitude of their combined momentum?

a) P1+P2
b) P1-P2
c) P2-P1
d)(P1P2)^(1/2)
e) (1/2)(P1+P2)
f)(P1+P2)^(1/2)
g)The answer depends on the directions in which the cars were moving before the collision.

4) Two cars collide inelastically and stick together after the collision. Before the collision, their momenta are p1 and p2. After the collision, their combined momentum is vector p. Of what can one be certain?

a) Vector P= p1+p2
b) Vector P= p1-p2
c) Vector P= p2-p1

aquamarineswan704

1. The Yukawa Potential energy function for the interaction ofneutrons and protons in a nucleus is . (a) What is the forceassociated with this potential energy? (b) If and Find the value ofthe force at r=a and at r=3a

2. For what value of the constant c is the forceconservative?

3. In a two-stage rocket, the exhaust velocity for the first stageburn is 3000 m/s and for the second stage burn is 3000 m/s. Assumethat during the entire sequence of burns the rocket is still nearenough to the surface of the earth to approximate the externalgravitational acceleration as 9.8m/s^2 , and ignore air resistance.The mass of the first stage engine and tanks is 2000kg. The mass ofthe fuel held in the first stage is 4000kg. The first stage fuelburns in 10 seconds. The first stage is then ejected. The mass ofthe second stage engine, tanks, and payload is 2000kg. The mass ofthe fuel held in the second stage is 2000kg. The second stage fuelburns in 5 seconds. (The second stage tanks remain attached to thepayload when empty.) (a) At what speed is the second stage/payloadcombination moving at the end of the second stage burn? (b) Howmuch faster is this than the speed if all the 6000kg fuel wereburned in the first stage in 15 seconds with the same exhaustvelocity (3000m/s) and the entire 4000kg assembly of the emptyrocket remained in one piece?

4. A particle with mass 10kg starts from rest at r = 10 and ?=0radians, following the trajectory given by r=10-2t , ?=0.2t. Findthe radial and angular components and of the force, as functions oftime, that will cause this motion

5. A sheet of material, mass 2kg, uniform density, is in the shapeof a right triangle bounded by the lines y=0, x=0, and y=4-x. Itattched to the origin, and free to rotate about the y axis. A forceof 1000 Newtons is applied perpendicular to the plane, located atthe x=4 point on the triangle as it starts to rotate. In aright-handed coordinate system, how fast will the object bespinning (in radians per second) as it crosses the y-z plane (thatis, when it has rotated through 270 degrees)?

Thank you in advanced.

Physics 197 Lecture Notes - Lecture 4: Particle System, Euclidean Vector, Weighted Arithmetic Mean

Physics 197 Full Course Notes

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