Question

All collisions will be completely elastic - that is, the total kinetic energy of the system will be constant throughout. Also, the collisions are entirely one-dimensional, with all motion taking place in either the northward or southward direction.

The setting: a room with a frictionless floor. A block of mass 1 kg is placed on the floor and initially pushed northward, whereupon it begins sliding with a constant speed of 5 m/s. It eventually collides with a secondary, stationary block of mass 4.5 kg, head-on, and rebounds back to the south.

A. What will be the speed of the 1-kg block after this collision?

Answer: -3.18 m/s

B. What will be the speed of the second heavier block after the collision?

Answer: 1.8 m/s

C. Now the first 1-kg block, after this first collision, slides south until it collides elastically with the southern wall of the room, bouncing off back to the north. The second block is still sliding northward at this point along the frictionless floor, at the same velocity imparted to it in part above (b) above. Eventually, the 1-kg block again collides with the second block. What will be the speed of the 1-kg block after this second collision?

Answer: 0.92 m/s

D. What will be the speed of the second block after this second collision?

Answer: 2.301

E. Assuming the room in question is very big, there is plenty of room for the blocks to both slide as far north as you might like. As you can imagine, for a while the 1-kg block will keep bouncing off the second block, then back off the southern wall, then back off the second block, and so on. But eventually, the 1-kg block will bounce off the southern wall with too low a speed to overtake the second block, and there will be no more collisions. At this point, how many collisions in total (including the first two described above) will there have been between the two blocks?

Please note: Part E is the only section that needs to be answered. Thorough explanations are greatly appreciated, Thank you so much!

Answer 1

Note- Collision with the wall does not change the magnitude of velocity of the block, it just reverses the direction of the velocity of the block.

So, after second collision as calculated by you, the first block will move north with speed of 0.92 m/s(+ve sign) whereas the second block with 2.301 second. Hence,they can never meet again and so,only two collisions are possible in total.