A 0.140 kg glider is moving to the right on a frictionless, horizontal air track

Question

A 0.140 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.730 m/s . It has a head-on collision with a 0.290 kg glider that is moving to the left with a speed of 2.21 m/s . Suppose the collision is elastic.

a) Find the magnitude of the final velocity of the 0.140 kg glider.

b) Find the direction of the final velocity of the 0.140 kg glider. (left or right)

c) Find the magnitude of the final velocity of the 0.290 kg glider.

d) Find the direction of the final velocity of the 0.290 kg glider. (left or right)

Explanation / Answer

here,

mass , m1 = 0.14 kgay u1 = 0.73 m/s

mass , m2 = 0.29 kg at u2 = - 2.21 m/s

let the final velocity be v1 and v2

using conservation of momentum

m1*u1 + m2*u2 = m1*v1 + m2*v2

0.14*0.73 - 0.29 * 2.21 = 0.14 * v1 + 0.29 * v2 ...(1)

using cosnervation of kinetic energy

0.5*m1*u1^2 + 0.5 * m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2

0.14*0.73^2 + 0.29 * 2.21^2 = 0.14 * v1^2 + 0.29 * v2^2 ...(2)

from (1) and (2)

v1 = - 3.24 m/s

v2 = - 0.3 m/s

a)

the magnitude of the final velocity of the 0.140 kg glider is 3.24 m/s

b)

the direction of the final velocity of the 0.140 kg glider towards left

c)

the magnitude of the final velocity of the 0.290 kg glider is 0.3 m/s

d)

the direction of the final velocity of the 0.290 kg glider to the left

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