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Objects A, B, and Care moving as shown in Fig. E8.3.Find the x- and y-components of the net momentum of the particlesif we define the system to consist of (a) Aand C, (b) Band C,(c) all three objects.

Short Answer

Expert verified

(a) The x component of the net momentum of the system consists of A and C is -3.0kg.m/s .

The y component of the initial momentum of the system consists of A and C is -55.0kg.m/s.

(b) The x component of the net momentum of the system consists of B and C is 0

The y component of the initial momentum of the system consists of B and C is 52kg.m/s.

(c) The x component of the net momentum of the system consists of A, B and C is 0.

The y component of the net momentum of the system consists of A, B and C is -3kg.m/s

Step by step solution

01

Given in the question

From the figure we can observe that,

Mass of the object A, mA=5.0kg

Velocity of object A,vA=vAy=-11m/s

Mass of the object B,mB=6.0kg

Velocity and angle of the object B, vB=10.0m/s,=60

Mass of the object C,mC=10kg

Velocity of the object C,vC=vCx=-3.0m/svC=vCx=-3.0m/s

02

Definition of momentum

A property of a moving body resulting from its mass and motion that is roughly equivalent to the product of its mass and velocity: a property of a moving body that determines how long it will take for it to come to rest when applied to a constant force.

03

Finding the x and y components of net momentum for part (a)

As we know the momentum of an object is

p=mv

If pxis x component of momentum and pyis y component of momentum

Then

px+py=mvx+mvy

Therefore,

The x-component of the net momentum of the system consists of A and C can be given as.

pAx+pCx=mAvAx+mcvcx=50kg0+10kg--3m/s=-30kg.m/s

The x component of the net momentum of the system consists of A and C is -30kg.m/s.

The y component of the net momentum of the system consists of A and C can be given as.

pAx+pCx=mAvAy+mcvcy=5kg-11m/s+10kg0=-55.0kg.m/s

The y component of the initial momentum of the system consists of A and C is -55.0kg/m/s

04

Finding the x and y components of net momentum for part (b)

Given in the question.

Mass of the object B,mB=6.0kg

Velocity and angle of the object B,vB=10.0m/s,=60

Therefore,

X-component of the velocity of object B, vBx=10.0cos60m/s

Y-component of velocity of the object B,vBy=10.0sin60m/s

Mass of object C,mC=10kg

Velocity of objectvC=vcx=-3.0m/s

The x component of the net momentum of the system consists of B and C can be given as.

pBx+pCx=mBvBx+mcvcx=6kg10cos60m/s+10kg-3m/s=30kg.m/s-30kg.m/s=0

The x component of the net momentum of the system consists of B and C is 0.

The y component of the net momentum of the system consists of B and C can be given as.

pBy+pCy=mBvBy+mcvcy=6kg10cos60m/s+10kg0=52kg.m/s

The y component of the net momentum of the system consists of B and C is 52kg.m/s .

05

Finding the x and y components of net momentum for part (C)

We know,

mA=5.0kgvA=vAy=-11m/smB=6.0kgvBx=10.0cos60m/svBy=10.0sin60m/smC=10kgvC=vCx=-3.0m/s

The x component of the net momentum of the system consists of A, B and C can be given as.

pAx+pBx+pCx=mAvax+mBvBx=5kg0+6kg10cos60m/s+10kg-3m/s=30kg.m/s-30kg.m/s=0

The x component of the net momentum of the system consists of A, B and C is 0 .

The y component of the net momentum of the system consists of A, B and C can be given as.

pAy+pBy+pCy=mAvay+mBvBy=5kg-11m/s+6kg10sin60m/s+10kg0=-55+52kg.m/s=-3kg.m/s

The y component of the net momentum of the system consists of A, B and C is -3kg.m/s .

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