PHY 101 1st Edition Lecture 17 Outline of Last Lecture I. Comparison: Impulse – Momentum Theorem vs. Work – Energy TheoremII. Relationship Between Kinetic Energy & MomentumOutline of Current Lecture III. 6.2 Conservation of MomentumIV. More on Conservation of MomentumV. 6.3 Collision in 1DVI. Perfectly Inelastic in 1DCurrent Lecture6.2 Conservation of Momentum- Pi = m1v1i + m2v2i before condition- Pf = m1v1f + m2v2f after condition- Law of conservation of momentum: total momentum of an isolated system is a constant- The momenta of individual objects in the systems any changes after a condition, but the vector summation of all momenta does not change- This is a direct consequence of Newton’s 3rd law: Action and reaction forces are always equal in magnitude, opposite in direction and act on different objects- During the collision:o Object 1 exerts a force F12 to object 2o Object 2 exerts a force F21 to object 1- Suppose the collision is a Δt- Apply the impulse-momentum theorem to object 1o F21Δt = Δp1 = m1v1f – m1v1i- Apply the impulse momentum theorem to object 2o F12Δt = Δp2 = m2v2f - m2v2i- According to Newton’s 3rd law:o F21 = -F12- We have F21Δt = -F12Δt- Therefore,o M1v1f – m1v1i = -(m2v2f – m2v2i)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Rearrange the equation:o M1v1f + m2v2f = m1v1i + m2v2i- The total momentum remains unchanged- Example:o An archer of mass 60kg stands at rest on frictionless ice. He fired a 0.5kg arrow horizontally at 50m/s.o What is the archer’s speed after he fires the arrow?o Solution: both the archer and the arrow have no initial speeds. Initial momentumof the system is zero. M1v1f + m2v2f = 0; m1v1f = -m2v2f V1f = -m2v2f/m1 = (0.5)(50)/60 = 0.42 m/s Recoil/ kickbackMore on Conservation of Momentum- M1v1f + m2v2f = m1v1i + m2v2i- After collision before collision- The total momentum is constant (doesn’t change)- Conservation of momentum only applied to isolated systems- A system is said to be isolated if there is no external force acting on it6.3 Collision in 1D- Collision: 2 objects move closer to each other and interact. They may or may not move apart after the collision- For an isolate systems:o The total momentum is conservedo The total KE may or may not stay the same- Different types of collisiono Elastic: a collision in which both momentum and KE are conservedo Inelastic: a collision in which only momentum is conserved- When 2 objects collide & stick together, the collision is “perfectly inelastic”- Momentum is always conserved for an isolated systems, regardless of type of collision- Example:o Elastic collision: billiard ball (approximately)o Inelastic collision: most macroscopic collision are inelastico Ex. A head- on collision of carso Before the collision Assuming m1 = m2, v1i = -v2i Total momentum: pi = 0 Total KE > 0o After the collision: V1f = v2f = 0, total momentum: pf = 0 Total KE = 0 (not conserved)o Where does the KE go?Perfectly Inelastic in 1D- Perfectly inelastic collision: two colliding bodies stick together after collision- The momentum is always conserved- Before collision p1 = m1v1 + m2v2i- After the collision, they stick together, have a common vf:o Pf = m1vf + m2vf = (m1 + m2)vf- Momentum conservation: pf = pio (m1 + m2)vf = m1v1i + m2v2i vf =( m1v1i + m2v2i)/(m1 +
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