Question

Two objects with different masses collide and bounce back after an elastic collision. Before the collision, the
two objects were moving at velocities equal in magnitude but opposite in direction. After the collision,
A. the less massive object had gained momentum.
B. the more massive object had gained momentum.
C. both objects had the same momentum.
D. both objects lost momentum.

Answer 1

Answer:A

Explanation:

Given

mass of two objects are  $m_1$ and $m_2$

taking $m_1>m_2$

Suppose $u_1$  and  $u_2$ are the velocities of $m_1$ and

$u_1=u$ and  $u_2=-u$

therefore after elastic collision velocity of $m_1$ and $m_2/[tex] are [tex]v_1$ and $v_2$

$v_1=\frac{m_1-m_2}{m_1+m_2}\cdot u_1+\frac{2m_2}{m_1+m_2}\cdot u_2$

$v_2=\frac{2m_1}{m_1+m_2}\cdot u_1-\frac{m_1-m_2}{m_1+m_2}\cdot u_2$

for $u_1$ and $u_2$

$v_1=\frac{m-m}{m+m}\cdot u+\frac{2m}{m+m}\cdot (-u)$

$v_1=\frac{m_1+m_2}{m_1+m_2}\cdot u=u$

$v_2=\frac{2m}{m+m}\cdot u-\frac{m-m}{m+m}\cdot (-u)$

$v_2=\frac{3m_1-m_2}{m_1+m_2}\cdot u$

$v_2=u+2\cdot \frac{m_1-m_2}{m_1+m_2}\cdot u$

so velocity of mass $m_2$ is more as compared to $m_1$

so less massive object gained some momentum

Answer 2

The more massive object will lose momentum after collision while the less massive object will gain momentum after collision.

• Let the mass of the first object = m₁
• Let the mass of the second object = m₂
• let the initial velocities of the two objects = u
• let the final velocity of the first object after collision = v₁
• Let the final velocity of the second object after collision = v₂

Apply the principle of conservation of linear momentum for elastic collision;

let the heavier object = m₁

m₁u + m₂(-u) = m₁(-v₁) + m₂v₂

m₁u  - m₂u = -m₁v₁ + m₂v₂

where;

m₁u and m₂u  are initial momentum of both objects before collision

m₁v₁ and  m₂v₂ are final momentum of both objects after collision

Thus, from the equation above we can conclude the following, the more massive object will lose momentum after collision while the less massive object will gain momentum after collision.

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