9 Linear Momentum and Collisions
9 Chapter Review
Key Terms
- center of mass
- weighted average position of the mass
- closed system
- system for which the mass is constant and the net external force on the system is zero
- elastic
- collision that conserves kinetic energy
- explosion
- single object breaks up into multiple objects; kinetic energy is not conserved in explosions
- external force
- force applied to an extended object that changes the momentum of the extended object as a whole
- impulse
- effect of applying a force on a system for a time interval; this time interval is usually small, but does not have to be
- impulse-momentum theorem
- change of momentum of a system is equal to the impulse applied to the system
- inelastic
- collision that does not conserve kinetic energy
- internal force
- force that the simple particles that make up an extended object exert on each other. Internal forces can be attractive or repulsive
- Law of Conservation of Momentum
- total momentum of a closed system cannot change
- linear mass density
- λλ, expressed as the number of kilograms of material per meter
- momentum
- measure of the quantity of motion that an object has; it takes into account both how fast the object is moving, and its mass; specifically, it is the product of mass and velocity; it is a vector quantity
- perfectly inelastic
- collision after which all objects are motionless, the final kinetic energy is zero, and the loss of kinetic energy is a maximum
- rocket equation
- derived by the Soviet physicist Konstantin Tsiolkovsky in 1897, it gives us the change of velocity that the rocket obtains from burning a mass of fuel that decreases the total rocket mass from mimi down to m
- system
- object or collection of objects whose motion is currently under investigation; however, your system is defined at the start of the problem, you must keep that definition for the entire problem
Key Equations
| Definition of momentum | [latex]\mathbf{\overset{\to }{p}}=m\mathbf{\overset{\to }{v}}[/latex] |
| Impulse | [latex]\mathbf{\overset{\to }{J}}\equiv {\int }_{{t}_{\text{i}}}^{{t}_{\text{f}}}\mathbf{\overset{\to }{F}}(t)dt\,\text{or}\,\mathbf{\overset{\to }{J}}={\mathbf{\overset{\to }{F}}}_{\text{ave}}\Delta t[/latex] |
| Impulse-momentum theorem | [latex]\mathbf{\overset{\to }{J}}=\Delta \mathbf{\overset{\to }{p}}[/latex] |
| Average force from momentum | [latex]\mathbf{\overset{\to }{F}}=\frac{\Delta \mathbf{\overset{\to }{p}}}{\Delta t}[/latex] |
| Instantaneous force from momentum (Newton’s second law) |
[latex]\mathbf{\overset{\to }{F}}(t)=\frac{d\mathbf{\overset{\to }{p}}}{dt}[/latex] |
| Conservation of momentum | [latex]\frac{d{\mathbf{\overset{\to }{p}}}_{1}}{dt}+\frac{d{\mathbf{\overset{\to }{p}}}_{2}}{dt}=0\enspace\text{or}\enspace{\mathbf{\overset{\to }{p}}}_{1}+{\mathbf{\overset{\to }{p}}}_{2}=\text{constant}[/latex] |
| Generalized conservation of momentum | [latex]\sum _{j=1}^{N}{\mathbf{\overset{\to }{p}}}_{j}=\text{constant}[/latex]