Question

A 3 kg block moving to the right on a frictionless table at 4 m/s makes a head on collision with another 3 kg block moving 5 m/s to the left. a) If the collision is completely inelastic, find the final velocity of the blocks. b) If the collision is completely elastic, find the final velocity of the blocks. c) If half the initial energy is dissipated in the collision, find the final velocities of the blocks.

Answer 1

a)

$$3(-4)+3(5)=(3+3)v\\v=0.5\frac{m}{s}$$

To the left.

b)

$$v_1=5\frac{m}{s}\text{ to the left}\\v_2=4\frac{m}{s}\text{ to the right}$$

c)

$$3(-4)+3(5)=3=3v_1-3v_2=3(v_1-v_2)\\ v_1-v_2=1\\K_f=0.5(0.5(3)(4)^2+0.5(3)(5)^2)\\=0.5(3)(v_1)^2+0.5(3)(v_2)^2\\30.75=1.5(v_1^2+(v_1-1)^2)\\v_1=3.66\frac{m}{s}\text{ to the left}\\v_2=2.66\frac{m}{s}\text{ to the right}$$