`color{red}✍️ ` The total momentum of an isolated system of interacting particles is conserved.
`\color{fuchsia} {★ \mathbf\ul"A bullet is fired from a gun"}`
Force on the bullet by the gun `=color{blue}{vecF}`
Force on the gun by the bullet `=color{blue}{ –vecF}`
According to the third law. The two forces act for a common interval of time Δt.
According to the second law,
Change in momentum of the bullet `=color{blue}{vecF Δt}`
Change in momentum of the gun `=color{blue}{– vecF Δt}`
`color{green}("Since initially, both are at rest, the change in momentum equals the final momentum for each.")`
Thus if `color{blue}{vecp_b}=` momentum of the bullet after firing
`color{blue}{vecp_g}=` recoil momentum of the gun
`vecp_g = – vecp_b`
i.e. `color{blue}{p_b + p_g = 0}`.
`color{green}{"That is, the total momentum of the (bullet + gun) system is conserved."}`
`color{red}✍️ ` An `color(red)("important example")` of the application of the law of conservation of momentum is the
`\color{fuchsia} {★ \mathbf\ul"Collision of two bodies"}`
Consider two bodies `A` and `B`, with initial momenta `color{blue}{vecp_A}` and `color{blue}{vecp_B}`.
The bodies collide, get apart, with final momenta `color{blue}{vec(p_A^')}` and `color{blue}{vec(p_B^')}` respectively.
`"By the Second Law,"`
`vecF_(AB)Δt = vec(p_A^') − vec(p_A)` and
`vecF_(BA)Δt = vec(p_B^') − vec(p_B)`
Since `color{red}{vecF_(AB) = −vecF_(BA)}` by the third law,
`vec(p_A^') − vec(p_A) = −(vec(p_B^') − vec(p_B) )`
i.e. `color{blue}{vec(p_A^') + vec(p_B^') = vec(p_A) + vec(p_B)}` which shows that
`color{green}{"the total final momentum of the isolated system equals its initial momentum."}`
`color{red}✍️ ` The total momentum of an isolated system of interacting particles is conserved.
`\color{fuchsia} {★ \mathbf\ul"A bullet is fired from a gun"}`
Force on the bullet by the gun `=color{blue}{vecF}`
Force on the gun by the bullet `=color{blue}{ –vecF}`
According to the third law. The two forces act for a common interval of time Δt.
According to the second law,
Change in momentum of the bullet `=color{blue}{vecF Δt}`
Change in momentum of the gun `=color{blue}{– vecF Δt}`
`color{green}("Since initially, both are at rest, the change in momentum equals the final momentum for each.")`
Thus if `color{blue}{vecp_b}=` momentum of the bullet after firing
`color{blue}{vecp_g}=` recoil momentum of the gun
`vecp_g = – vecp_b`
i.e. `color{blue}{p_b + p_g = 0}`.
`color{green}{"That is, the total momentum of the (bullet + gun) system is conserved."}`
`color{red}✍️ ` An `color(red)("important example")` of the application of the law of conservation of momentum is the
`\color{fuchsia} {★ \mathbf\ul"Collision of two bodies"}`
Consider two bodies `A` and `B`, with initial momenta `color{blue}{vecp_A}` and `color{blue}{vecp_B}`.
The bodies collide, get apart, with final momenta `color{blue}{vec(p_A^')}` and `color{blue}{vec(p_B^')}` respectively.
`"By the Second Law,"`
`vecF_(AB)Δt = vec(p_A^') − vec(p_A)` and
`vecF_(BA)Δt = vec(p_B^') − vec(p_B)`
Since `color{red}{vecF_(AB) = −vecF_(BA)}` by the third law,
`vec(p_A^') − vec(p_A) = −(vec(p_B^') − vec(p_B) )`
i.e. `color{blue}{vec(p_A^') + vec(p_B^') = vec(p_A) + vec(p_B)}` which shows that
`color{green}{"the total final momentum of the isolated system equals its initial momentum."}`