Question

Block A is initially moving to the right at 6.00 m/s, while block B is initially at rest. The surface they move on is level and frictionless. What is the velocity of the center of mass of the two blocks after the blocks collide

Answer 1

Complete question:

Block A on the left has a mass of 1.0 kg, Block B on the right has a mass of 3.0 kg.

Block A is initially moving to the right at 6.00 m/s, while block B is initially at rest. The surface they move on is level and frictionless. What is the velocity of the center of mass of the two blocks after the blocks collide

Answer:

The velocity of center mass of the two blocks after collision is 1.5 m/s to the right.

Explanation:

Let the mass of block A = m₁ = 1 kg

Let the mass of block B = m₂ = 3kg

initial velocity of block A, u₁ = 6 m/s

initial velocity of block B, u₂ = 0

let the velocity of center mass of the blocks after collision = v

Apply the principle of conservation of linear momentum for inelastic collision (the two blocks sticked together after collision);

$m_1u_1 + m_2u_2 = v(m_1+m_2)\\\\m_1u_1 + m_2(0) = v(m_1+m_2)\\\\m_1u_1 = v(m_1+m_2)\\\\v = \frac{m_1u_1}{m_1+m_2}\\\\v= \frac{1*6}{1+3}\\\\v= \frac{6}{4}\\\\v= 1.5 \ m/s \ \ \ to \ the \ right$

v = 1.5 m/s to the right

Therefore, the velocity of center mass of the two blocks after collision is 1.5 m/s to the right.