A trolley P of mass 4.0\text{ kg} moving due east at 5.0\text{ m s}^{-1} collides head-on … — JAMB UTME

A trolley P of mass $4.0\text{ kg}$ moving due east at $5.0\text{ m s}^{-1}$ collides head-on with a trolley Q of mass $1.0\text{ kg}$ moving due west at $10.0\text{ m s}^{-1}$ . If the two trolleys coalesce upon impact, what is their common velocity?

$2.0\text{ m s}^{-1}$ due eastCevap
B
$6.0\text{ m s}^{-1}$ due east
C
$2.5\text{ m s}^{-1}$ due east
D
$1.0\text{ m s}^{-1}$ due east

Cevap

2.0\text{ m s}^{-1}

due east

Linear momentum is conserved in an isolated system. Taking east as positive, the initial momentum of trolley P is

+20.0\text{ kg m s}^{-1}

and trolley Q is

-10.0\text{ kg m s}^{-1}

, yielding a net initial momentum of

+10.0\text{ kg m s}^{-1}

. After impact, the total mass is

4.0\text{ kg} + 1.0\text{ kg} = 5.0\text{ kg}

. The common velocity is

\frac{10.0}{5.0} = +2.0\text{ m s}^{-1}

, where the positive sign denotes a direction due east.

Adım Adım Çözüm

Assign a directional coordinate system

Let the eastward direction be positive (

+

) and the westward direction be negative (

-

)

Linear momentum is a vector quantity, so opposite directions must have opposite signs.

Calculate total initial momentum (

p_i

)

p_i = m_P u_P + m_Q u_Q = (4.0 \times 5.0) + (1.0 \times (-10.0)) = 20.0 - 10.0 = +10.0\text{ kg m s}^{-1}

According to the principle of conservation of linear momentum, initial momentum equals final momentum.

Calculate final common velocity (

v

)

v = \frac{p_i}{m_P + m_Q} = \frac{+10.0}{4.0 + 1.0} = +2.0\text{ m s}^{-1}

Since the trolleys coalesce, they move together with a total combined mass of

5.0\text{ kg}

Anahtar Kavram

Conservation of Linear Momentum in 1D Inelastic Collisions

Soru

Cevap

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