Answer to Question #198771 in Mechanics | Relativity for karen

Question

Two blocks of mass 300 g and 200 g respectively are moving toward each other along a horizontal frictionless surface with velocities of 50 cm/s and 100 cm/s, respectively. a. If the blocks collide and stick together, find their final velocity. (5 pts.) b. Find the final velocity of each block if the collision is completely elastic (e =1).

Answer 1

Gives

$m_1=300g=0.3kg$

$m_2=200g=0.2kg$

$u_1=50cm/sec=0.50cm/sec$

$u_2=100cm/sec=1m/sec$

$v=?$

Momentum conservation

$m_1u_1+m_2u_2=(m_1+m_2)v$

$v=\frac{m_1u_1+m_2u_2}{m_2+m_2}$

$$v=\frac{0.3\times0.50+0.2\times1}{0.3+0.2}=0.7m/sec$$

(b)

Momentum conservation in elastic collision

$m_1u_1+m_2u_2=(m_1v_1+m_2v_2)$

$$0.3\times0.5-0.2\times1=0.3v_1+0.2v_2$$

$0.3v_1+0.2v_2=0.15-0.2$

$0.3v_1+0.2v_2=-0.05\rightarrow(1)$

elastic collision

e=1

$v_2-v_1=u_1-u_2$

$v_2-v_1=0.5+1=1.5\rightarrow(2)$

eqution (1)and(2)

$v_2=80cm/sec$

$v_1=-70cm/sec$