A car, mass m 1 is moving to the right on a frictionless air track. It collides

Question

A car, mass m1 is moving to the right on a frictionless air track. It collides with a second car, mass m2, which is initially at rest. Which of the following statements are true? (If A and E are true, and the others are not, enter TFFFT).

A) If car 1 sticks to car 2, the car1-car2 system must move to the right after the collision.
B) Suppose (for this statement only) that car 2 was NOT initially at rest, but was instead heading towards car 1 with equal (but opposite) momentum before the collision. After the collision, the cars must both be at rest.
C) If the collision is elastic, car 1 must always come to a stop after the collision.
D) If car 1 sticks to car 2, the final total kinetic energy of the car1-car2 system is equal to the initial total kinetic energy of the two cars.
E) If car 1 is much lighter than m2, and the collision is perfectly elastic, car 1 will continue heading to the right with nearly its original speed after the collision.

Explanation / Answer

ELASTIC COLLISION

mass of car 1 = m1

mass of car 2 = m2

velocity before collision

velocity of car 1 = v1i

velocity of car 2 = v2i

velocity after collision

velocity of car 1 = v1f

velocity of car 2 = v2f

initial momentum before collision

Pi = m1*v1i + m2*v2i

after collision final momentum

Pf = m1*v1f + m2*v2f

from momentum conservation

total momentum is conserved

Pf = Pi

m1*v1i + m2*v2i = m1*v1f + m2*v2f .....(1)

from energy conservation

total kinetic energy before collision = total kinetic energy after collision

KEi = 0.5*m1*v1i^2 + 0.5*m2*v2i^2

KEf =   0.5*m1*v1f^2 + 0.5*m2*v2f^2

KEi = KEf

0.5*m1*v1i^2 + 0.5*m2*v2i^2 = 0.5*m1*v1f^2 + 0.5*m2*v2f^2 .....(2)

solving 1&2

we get

v1f = ((m1-m2)*v1i + (2*m2*v2i))/(m1+m2)

v2f = ((m2-m1)*v2i + (2*m1*v1i))/(m1+m2)

INELASTIC

m1*v1i + m2*v2i = (m1 + m2)*Vf

A)

v2i = 0

m1*v1i is positive

vf is positive

TRUE

------------------

B)

initial momentum Pi = P1i + P2i

P2i = -P1i

Pi = 0

therfore Pf = P1f + P2f = 0

P1f = -P2f

FALSE

--------------

C)

In elastic collision

if m1 = m2

v1f = 0

here m1 is not equal to m2

FALSE

D)

IN INELASTIC COLLISION the totla kinetic energy is not conserved

FALSE

E)

m1 <<<< m2

m1 - m2 = -m2

m1 + m2 = m2

v1f = (-(m2*v1i) + 0 )(m2)

v1f = -v1i

car 1 moves back with its original speed

FALSE

TFFFF

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