A bullet with a mass of 5 gramsand speed of 560 m/sis fired horizontally atablock of wood with a mass of 2 kg. The block rests on a frictionless horizontal surface.The bullet hits and gets stuck in the block. which one of the following is correct?
A. Only momentum is conserved
B. Only kinetic energy is conserved
C. Neither momentum nor kinetic energy is conserved
D. Both, momentum and kinetic energy are conserved
Question
Momentum is conserved if and only if sum of all forces which are exserted on system equals zero. In our situation there are only internal forces, so by Newton’s third law their vector sum is 0.
So [tex]mv=(m+M)v’ \Leftrightarrow v’=\frac{mv}{m+M}[/tex].
Kinetic energy of system at first: [tex]\frac{mv^2}{2}=784\;\textbf{J}[/tex]. After: [tex]\frac{(m+M)\frac{m^2v^2}{(m+M)^2} }{2}=\frac{m^2v^2}{2(m+M)}\approx 1,96\; \textbf{J}[/tex]. The secret is that other energy is in work of deformation forces (they in turn heat a bullet and a block).
Answer is A)