Question

Speed amplifier. In the figure block 1 of mass m₁ slides along an x axis on a frictionless floor at speed 0.568 m/s. Then it undergoes a one-dimensional elastic collision with stationary block 2 of mass m₂ = 0.284 m₁. Next, block 2 undergoes a one-dimensional elastic collision with stationary block 3 of mass m₃ = 0.522 m₂. (a) What then is the speed of block 3? Compute ratios of (b) speeds, (c) kinetic energies, and (d) momentums for block 3 to block 1.

Answer 1

Solution:

Case 1.   collides with .

Let and be the speeds of and before collision. After collision, their speeds be and . Given,

, & .

By the Law of conservation of momentum,

...................(1)

By the Law of conservation of energy,

   ...........(2)

From (1) & (2) and on substituting , we get,

The speed of after collision is .

Case 2. collides with .

Let and be the speeds of and before collision. After collision, let their speeds be & . Given,

, & .

From the laws of conservation of momentume and energy,

.......................(3)

   ...............(4)

From (3) & (4) and on substituting ,

(a) The speed of block 3 () after collision is

(b) Ratio of speeds of block 3 to block 1

(c) Ratio of kinetic energies of block 3 to block 1

  

(d) Ratio of momentum of block 3 to block 1