Question

A 16-g mass is moving in the +x direction at 30 cm/s while a 4-g mass is moving in the -x direction at 50 cm/s. They collide head on and stick together. Find their velocity after the collision.

a) 17.65 cm/s in the +x direction
b) 47.06 cm/s in the -x direction
c) 23.53 cm/s in the +x direction
d) 35.29 cm/s in the -x direction

Answer 1

The final velocity of two masses that collide head-on and stick together is 14 cm/s in the +x direction, calculated using the conservation of momentum principle.

Step-by-step explanation:

The student is asking about the velocity of two masses after a head-on collision in which they stick together. This is a classic physics problem that involves the conservation of momentum. Since momentum before the collision must equal momentum after the collision (when no external forces are acting on the system), the formula to use here is m1*v1 + m2*v2 = (m1 + m2)*v_final, where m1 and m2 are the masses, v1 and v2 are the initial velocities, and v_final is the final velocity after the collision.

To solve this, first convert the masses into kilograms: 16 g = 0.016 kg and 4 g = 0.004 kg. Then plug the values into the momentum conservation equation:

0.016 kg * 30 cm/s + 0.004 kg * (-50 cm/s) = (0.016 kg + 0.004 kg) * v_final

v_final = (0.016 kg * 30 cm/s - 0.004 kg * 50 cm/s) / (0.016 kg + 0.004 kg)

v_final = (0.48 kg*cm/s - 0.2 kg*cm/s) / 0.02 kg

v_final = 0.28 kg*cm/s / 0.02 kg

v_final = 14 cm/s in the +x direction.