Car A, with mass mA, moves west at speed vA, while car B, with mass mB, moves no

Question

Car A, with mass mA,  moves west at speed vA, while car B, with mass mB, moves north at speed vB. The two cars hit each other and get stuck together. Use a reference frame with the positive x-axis pointing due-east and the positive y-axis pointing due-north:

a) Find the velocity (vector) of the two cars after the collision.
b) Find the final combined kinetic K energy of the two cars.
c) Find the velocity (vcm) of the center of mass of the two cars before the collision.

Show your work. Write your result in terms of mA, vA, mB, and vB.

Explanation / Answer

a) velocity of car A = vA (-i) = -vA i

velocity of car B = vB j

using momentum conservation,

mA * (-vA i) + mB vB j = (mA + mB) Vf

vf = -(mAvA / (mA +mB)) i + (mBvB / (mA +mB)) j

b) magnitude = sqrt [ (mAvA / (mA +mB))^2 + (mBvB / (mA +mB))^2 ]

combined k.E. = mv^2 /2

= (mA + mB) ( (mAvA / (mA +mB))^2 + (mBvB / (mA +mB))^2 ) /2

= mA^2 vA^2 + mB^2 vB^2 / 2(mA +mB)

c) velocity of centre of mass

= (mA(-vA)i + mB vBj ) / (mA +mB)

= -(mAvA / (mA +mB)) i + (mBvB / (mA +mB)) j

c)

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

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