Question

Block 1, of mass m1 = 9.50 kg , moves along a frictionless air track with speed v1 = 25.0 m/s . it collides with block 2, of mass m2 = 41.0 kg , which was initially at rest. the blocks stick together after the collision. What is the final velocity of the combined blocks?

1) 10.0 m/s
2) 15.0 m/s
3) 20.0 m/s
4) 30.0 m/s

Answer 1

The final velocity of the combined blocks after a completely inelastic collision is calculated using conservation of momentum. The calculated velocity (approximately 5.68 m/s) does not match any of the provided options exactly, suggesting an error in the question options. The closest option is 10.0 m/s.

Step-by-step explanation:

The problem describes a collision between two blocks where after the collision, the blocks stick together. This type of collision is known as a completely inelastic collision. In an inelastic collision, momentum is conserved but kinetic energy is not. To find the final velocity of the combined masses after the collision, we apply the conservation of momentum principle.

Therefore, the final velocity v_f is closest to option 1) 10.0 m/s, considering the provided options. However, none of the options exactly match the calculated velocity of 5.68 m/s. This suggests there might be an error in the options provided or a misprint, as the correct final velocity should be slightly more than half the initial velocity of the smaller mass due to the significant increase in combined mass after the collision.