Secure https 902782958offetnext em 8 C 8 of 117 Belore you use the center of mas

Question

Secure https 902782958offetnext em 8 C 8 of 117 Belore you use the center of mass approach, you should first understand the tolowing terms System Any collection ofl objects that are of interest to you in a partcular sduaton In manoblemes, you have a certain freedom in choosing your system Making a wise choice for the system is often the irst step in solving the problem effioenty Center of mass The point that sepresents the "average" postion of the entive mass of a system. The postion of the center of mass can be expressed in tems of the postion vectors F of the particles as Learning Goal: Understand thal, for many purposes, a system can be treated as a point ike particle with its mass concentraled at e center of mass A complex systom of objects, both poind-lke and extended ones can offen be treated as a poit particle, lcated at the systems center of mass Such an approach can grealy simplity probiom soving The x coordnahe of the center of mass can be expressed in tarims of thex cooednates (ra), of the prtcles n Simlarly, the y coordinale of the center of mass can be expressed External force Any force acting on an object inside your system that results from an interaction with an object outside your system Consider a system of two blocks that have masses m and m Assume thai the blocks are poiet-ske particles and are locatod along the x axis at the coordnales ?1and 27 as shown origino 1) In this prelem tho blocks can only move along the raes Figure Part A Express your answer in terms oft m,i,, and t

Explanation / Answer

a)

center of mass of the system is given as

xcm = (m1 x1 + m2 x2)/(m1 + m2)

b)

to the left of m2 with distance much less that x2 - x1

c)

half way between m1 and m2

d)

xcm = (m1 x1 + m2 x2)/(m1 + m2)

taking derivative both side relative to "t"

dxcm /dt = (m1 (dx1/dt) + m2 (dx2?/dt))/(m1 + m2)

(vcm)x = (m1 v1x + m2 v2x)/(m1 + m2)

e)

v1x = - v2x

(vcm)x = (m1 (- v2x) + m2 v2x)/(m1 + m2)

(vcm)x = 0

f)

(vcm)x = (m1 v1x + m2 v2x)/(m1 + m2)

(vcm)x = (P1x + P2x)/(m1 + m2)

g)

0 = (P1x + P2x)/(m1 + m2)

P1x = - P2x

hence

|P1x| = |P2x|

f)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.