Question

A block of mass m slides with a speed vo on a frictionless surface and collides with another mass M which is initially at rest. The two blocks stick together and move with a speed of vo /3. In terms of m, mass M is most nearly_____.

Answer 1

To solve this problem we will apply the concepts related to the conservation of momentum. Momentum can be defined as the product between mass and velocity. We will depart to facilitate the understanding of the demonstration, considering the initial and final momentum separately, but for conservation, they will be later matched. Thus we will obtain the value of the mass. Our values will be defined as

$m_1 = m$

$m_2 = M$

$v_{1i} =v_0$

$v_{2i} = 0$

Initial momentum will be

$P_i = m_iv_{1i}+m_2v_{2i}$

$P_i = mv_0$

After collision

$v_{1f} = v_{2f} = \frac{v_0}{3}$

Final momentum

$P_f = (m_1+m_2)(\frac{v_0}{3})$

$P_f = (m+M)(\frac{v_0}{3})$

From conservation of momentum

$P_f = P_i$

Replacing,

$(m+M)(\frac{v_0}{3})=mv_0$

$(m+M)\frac{1}{3} = m$

$m+M=3m$

$M=3m-m$

$M=2m$