Question

In a physics experiment, two equal-mass carts roll towards each other on a level, low-friction track. One cart rolls rightward at 2 m/s and the other cart rolls leftward at 1 m/s. After the carts collide, they couple (attach together) and roll together with a speed of __________. Ignore resistive forces.a. 0.5 m/s
b. 0.33 m/s
c. 0.67 m/s
d. 1.0 m/s
e. none of these

Answer 1

Answer:

The correct answer is option a.

Explanation:

Conservation of momentum :

$m_1u_1+m_2u_2=m_1v_1+m_1v_2$

Where :

$m_1, m_2$ = masses of object collided

$u_1,u_2$ = initial velocity before collision

$v_1,v_2$ = final velocity after collision

We have :

Two equal-mass carts roll towards each other.

$m_1=m_2=M$

Initial velocity of $m_1=u_1=2 m/s$

Initial velocity of $m_2=u_2=-1 m/s$ (opposite direction)

Final velocity of $m_1=v_1=v$ (same direction )

Final velocity of $m_2=v_2=v$  (same direction)

$M\times 2 m/s+M(-1 m/s)=Mv+Mv$

$1 m/s=2v$

v = 0.5 m/s

rg135

The speed of the carts after their collision is 0.5 m/s.